Bevacizumab With or Without Fosbretabulin Tromethamine in Treating Patients With Recurrent or Persistent Ovarian Epithelial, Fallopian Tube, or Peritoneal Cavity Cancer

Inclusion Criteria: * Patients must have recurrent or persistent epithelial ovarian, fallopian tube, or primary peritoneal carcinoma; histologic documentation of the original primary tumor is required via the pathology report * Patients must have measurable disease or detectable (non-measurable) disease: * Measurable disease defined as at least one lesion that can be accurately measured in at least one dimension (longest dimension to be recorded); each lesion must be \>= 10 mm when measured by computed tomography (CT) scan, magnetic resonance imaging (MRI) or caliper measurement by clinical exam, or \>= 20 mm when measured by chest x-ray; lymph nodes must be \>= 15 mm in short axis when measured by CT or MRI * Detectable disease in a patient is defined as one who does not have measurable disease but has at least one of the following conditions: * Baseline values of CA-125 at least 2 x upper limit of normal (ULN) * Ascites and/or pleural effusion attributed to tumor * Solid and/or cystic abnormalities on radiographic imaging that do not meet RECIST 1.1 definition for target lesions * Patients in the measurable disease cohort must have at least one ?target lesion? to be used to assess response on this protocol as defined by RECIST 1.1; tumors within a previously irradiated field will be designated as ?non-target? lesions unless progression is documented or a biopsy is obtained to confirm persistence at least 90 days following completion of radiation therapy * Patients must not be eligible for a higher priority Gynecologic Oncology Group (GOG) protocol, if one exists; in general, this would refer to any active GOG phase 3 protocol or rare tumor protocol for the same patient population * Patients who have had one prior treatment must have a performance status of 0, 1, or 2 * Patients who have had two or three prior treatments must have a performance status of 0 or 1 * Patients should be free of acute hepatitis and active infection requiring parenteral antibiotics (with the exception of uncomplicated urinary tract infection \[UTI\]) * Recovery from the effects of recent surgery, radiotherapy, or chemotherapy * Any hormonal therapy directed at the malignant tumor must be discontinued at least one week prior to registration * Any other prior therapy directed at the malignant tumor, including chemotherapy, biological/targeted and immunologic agents, must be discontinued at least 3 weeks prior to registration (including small molecules and murine monoclonal antibodies); chimeric or human or humanized monoclonal antibodies (including bevacizumab) or vascular endothelial growth factor (VEGF) receptor fusion protein (including VEGF Trap/aflibercept) must be discontinued for at least 12 weeks prior to registration; no investigational therapy within 30 days prior to the first date of study treatment * Any prior radiation therapy must be discontinued at least 4 weeks prior to registration * Prior therapy: * Patients must have had one prior platinum-based chemotherapeutic regimen for management of primary disease containing carboplatin, cisplatin, or another organoplatinum compound; this initial treatment may have included intraperitoneal therapy, consolidation, non-cytotoxic (biologic/targeted agents, such as bevacizumab) or extended therapy administered after surgical or non-surgical assessment * Patients are allowed to receive, but are not required to receive, two additional cytotoxic regimens for management of recurrent or persistent disease, with no more than 1 non-platinum, non-taxane regimen * Patients are allowed to receive, but are not required to receive, non-cytotoxic (biologic/targeted agents, such as bevacizumab) therapy as part of their primary treatment regimen; patients must have NOT received any non-cytotoxic therapy (biologic/targeted agents) for management of recurrent or persistent disease (e.g., GOG protocol 170 series drugs or bevacizumab) * For the purposes of this study, poly (adenosine diphosphate \[ADP\]-ribose) polymerase (PARP) inhibitors will be considered ?cytotoxic?, and prior treatment with PARP inhibitors for primary or recurrent disease WILL be allowed (either alone or in combination with chemotherapy) * Patients with both platinum-sensitive and platinum-resistant disease are eligible; patients with platinum-refractory disease are NOT eligible; platinum-refractory disease is defined as patients who have progression of disease during the preceding platinum treatment * Definitions: * Platinum-free interval (PFI) is the period of time from the date of last platinum therapy to the date of progression (recurrence by CA-125, CT, etc.; CT is preferred) of disease or initiation of subsequent therapy (whichever occurs first); non-platinum maintenance therapy (e.g., extending taxane treatment) is excluded as a ?subsequent therapy;? if the patient?s last regimen used platinum, and she has NOT progressed before enrolling onto this study, then her PFI will be calculated from the date of last platinum therapy to the date of registration onto this study * PFI for the most recent platinum therapy will need to be calculated before enrollment onto this study for stratification purposes (i.e. balanced randomization) * Patients who have a PFI =\< 182 days (26 weeks) are defined as ?platinum resistant;? patients who have 182 \< PFI =\< 365 days are defined as ?GOG platinum sensitive;? finally, patients with PFI \> 365 days are defined as ?platinum sensitive? * ANC greater than or equal to 1,500/mcl * Platelets greater than or equal to 100,000/mcl * Hemoglobin greater than or equal to 9 g/dL * Creatinine less than or equal to 1.5 x institutional upper limit of normal (ULN) * Potassium within the normal reference range for the laboratory; correction with supplements is acceptable * Magnesium within the normal reference range for the laboratory; correction with supplements is acceptable * Calcium within the normal reference range for the laboratory; correction with supplements is acceptable * Bilirubin less than or equal to 1.5 x ULN * Serum glutamic oxaloacetic transaminase (SGOT) (aspartate aminotransferase \[AST\]) =\< less than or equal to 3 x ULN * Alkaline phosphatase less than or equal to 2.5 x ULN * Prothrombin time (PT) such that international normalized ratio (INR) is less than or equal to 1.5 x ULN (or an in-range INR, usually between 2 and 3, if a patient is on a stable dose of therapeutic warfarin) and a partial thromboplastin time (PTT) less than or equal to 1.5 x ULN * Urine protein should be screened by urine analysis; if protein is 2+ or higher, a 24-hour urine protein should be obtained and the level must be \< 1,000 mg (\< 1.0 g/24 hrs) for patient enrollment * Patients of childbearing potential must have a negative serum pregnancy test prior to the study entry and be practicing an effective form of contraception * Patients must have signed an approved informed consent and authorization permitting the release of personal health information * Patients must meet pre-entry requirements Exclusion Criteria: * Patients who have received prior fosbretabulin tromethamine or any other vascular disrupting agent (VDA) * Patients with other invasive malignancies, with the exception of non-melanoma skin cancer and other specific malignancies as noted below, are excluded if there is any evidence of other malignancy being present within the last three years; patients are also excluded if their previous cancer treatment contraindicates this protocol therapy * Patients who have received prior radiotherapy to any portion of the abdominal cavity or pelvis OTHER THAN for the treatment of ovarian, fallopian tube or primary peritoneal cancer within the last three years are excluded; prior radiation for localized cancer of the breast, head and neck, or skin is permitted, provided that it was completed more than three years prior to registration, and the patient remains free of recurrent or metastatic disease * Patients who have received prior chemotherapy for any abdominal or pelvic tumor OTHER THAN for the treatment of ovarian, fallopian tube or primary peritoneal cancer within the last three years are excluded; patients may have received prior adjuvant chemotherapy for localized breast cancer, provided that it was completed more than three years prior to registration, and the patient remains free of recurrent or metastatic disease * Patients with serious non-healing wound, ulcer, or bone fracture; this includes history of abdominal fistula, gastrointestinal perforation or intra-abdominal abscess within 90 days prior to the first date of study treatment * Patients with active bleeding or pathologic conditions that carry high risk of bleeding, such as known bleeding disorder, coagulopathy, or tumor involving major vessels * Patients with history or evidence upon physical examination of central nervous system (CNS) disease, including primary brain tumor, seizures not controlled with standard medical therapy, any brain metastases, or history of cerebrovascular accident (CVA, stroke), transient ischemic attack (TIA) or subarachnoid hemorrhage within six months prior to the first date of treatment on this study * Patients with clinically significant cardiovascular disease; this includes: * Uncontrolled hypertension, defined as systolic \> 150 mm Hg or diastolic \> 90 mm Hg despite antihypertensive medications * History of torsade de pointes, ventricular tachycardia or fibrillation, pathologic sinus bradycardia (\< 60 beats per minute \[bpm\]), heart block (excluding 1st degree block being, PR interval prolongation only), congenital long QT syndrome, new ST segment elevation or depression, or new Q waves on electrocardiogram (ECG) * Patients with corrected QT interval (QTc) \> 470 msec * Requirement for receiving any drug known to prolong the QTc interval, including anti-arrhythmic medications; stable regimen of antidepressants of the selective serotonin reuptake inhibitor (SSRI) class is allowed * Myocardial infarction or unstable angina within 6 months prior to registration * New York Heart Association (NYHA) class II or greater congestive heart failure * Serious cardiac arrhythmia requiring medication; this does not include asymptomatic, atrial fibrillation with controlled ventricular rate * Patients who have received prior treatment with an anthracycline (including doxorubicin and or pegylated liposomal doxorubicin \[Doxil; PLD\]) must have an echocardiogram assessment and are excluded if they have an ejection fraction \< 50% * Common Terminology Criteria for Adverse Events (CTCAE) grade 2 or greater peripheral vascular disease (at least brief \[\< 24 hrs\] episodes of ischemia managed non-surgically and without permanent deficit) * Known hypersensitivity to any of the components of fosbretabulin tromethamine or bevacizumab * Major surgery within 28 days prior to the first date of study treatment * Anticipation of need for major surgical procedures during the course of the study * Core biopsy within 7 days prior to the first date of study treatment * Patients with clinical symptoms or signs of gastrointestinal obstruction and patients who require parenteral hydration and/or nutrition; patients with bowel involvement on CT scan * Patients with medical history or conditions not otherwise previously specified which in the opinion of the investigator should exclude participation in this study; the investigator can consult the Study Chair or Study Co-Chairs for uncertainty in this regard * Patients who are pregnant or nursing