Paclitaxel and Cisplatin or Topotecan With or Without Bevacizumab in Treating Patients With Stage IVB, Recurrent, or Persistent Cervical Cancer

Inclusion Criteria: * Patients must have primary stage IVB, recurrent or persistent squamous cell carcinoma, adenosquamous carcinoma, or adenocarcinoma of the cervix which is not amenable to curative treatment with surgery and/or radiation therapy * All patients must have measurable disease; measurable disease is 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 \>= 20 mm when measured by conventional techniques, including palpation, plain x-ray, computed tomography (CT), and magnetic resonance imaging (MRI), or \>= 10 mm when measured by spiral CT; biopsy confirmation is required if the lesion(s) measures \< 30 mm or if the treating physician determines it is clinically indicated; patients must have at least one "target lesion" to be used to assess response on this protocol as defined by Response Evaluation Criteria in Solid Tumors (RECIST); this lesion should be the one that was biopsied if one was performed; 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 * Absolute neutrophil count (ANC) \>= 1500/mcl * Platelets \>= 100,000/mcl * Serum creatinine =\< upper limit of normal (ULN) (Common Toxicity Criteria \[CTC\] grade 0) or calculated creatinine clearance (Jeliffe formula) \>= 60 ml/min * Bilirubin =\< 1.5 x institutional normal * Serum glutamic oxaloacetic transaminase (SGOT) =\< 2.5 x institutional normal * Alkaline phosphatase =\< 2.5 x institutional normal * Prothrombin time (PT) such that international normalized ratio (INR) is =\< 1.5 (or an in-range INR, usually between 2 and 3, if a patient is on a stable dose of therapeutic warfarin for management of venous thrombosis including pulmonary thrombo-embolus) * Partial thromboplastin time (PTT) \< 1.2 times the upper limit of normal * Urine protein-creatinine ratio (UPC ratio) \< 1.0 * Patients must have a GOG performance status of 0 or 1 * Patients must have recovered from the effects of surgery, radiation therapy, or chemoradiotherapy; at least six weeks must have elapsed from the last administration of chemoradiotherapy, and at least three weeks must have elapsed from the last administration of radiation therapy alone; at least six weeks must have elapsed from the time of any major surgical procedure prior to randomization * Patients must have signed an approved informed consent and authorization permitting release of personal health information * Patients must meet all of the pre-entry requirements, including baseline QOL questionnaire * Patients must be free of active infection requiring antibiotics Exclusion Criteria: * Patients with bilateral hydronephrosis which cannot be alleviated by ureteral stents or percutaneous drainage * Patients previously treated with chemotherapy except when used concurrently with radiation therapy * Patients who have received concurrent paclitaxel and/or concurrent topotecan with radiation therapy are ineligible * Patients with craniospinal metastases * Patients with a concomitant malignancy other than non-melanoma skin cancer * Patients with a prior invasive malignancy (except non-melanoma skin cancer) who have had any evidence of disease within the last 5 years or whose prior malignancy treatment contraindicates the current protocol therapy * Patients with serious non-healing wound, ulcer, or bone fracture; this includes history of abdominal fistula, gastrointestinal perforation or intra-abdominal abscess for which an interval of 3 to 6 months must pass before study entry; in addition, the patient must have undergone correction (or spontaneous healing) of the perforation/fistula and/or the underlying process causing the fistula/perforation; patients with granulating incisions healing by secondary intention with no evidence of fascial dehiscence or infection are eligible but require weekly wound examinations * 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 of 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 * Myocardial infarction or unstable angina \< 6 months prior to registration * New York Heart Association (NYHA) grade II or greater congestive heart failure * Serious cardiac arrhythmia requiring medication; this does not include asymptomatic, atrial fibrillation with controlled ventricular rate * CTCAE grade 2 or greater peripheral vascular disease (at least brief \[\< 24 hours (hrs)\]) episodes of ischemia managed non-surgically and without permanent deficit) * History of CVA within six months * Patients with known hypersensitivity to Chinese hamster ovary cell products or other recombinant human or humanized antibodies * Patients with or with anticipation of invasive procedures as defined below: * Major surgical procedure, open biopsy or significant traumatic injury within 28 days prior to the first date of bevacizumab therapy * Major surgical procedure anticipated during the course of the study; this includes, but is not limited to abdominal surgery (laparotomy or laparoscopy) prior to disease progression, such as colostomy or enterostomy reversal, interval or secondary cytoreductive surgery, or second look surgery; please consult with the study chair prior to patient entry for any questions related to the classification of surgical procedures * Core biopsy, within 7 days prior to randomization * Patients who are pregnant or nursing; bevacizumab should not be administered to pregnant women; bevacizumab should not be administered to nursing women; patients of childbearing potential must agree to use contraceptive measures during study therapy and for at least six months after completion of bevacizumab therapy * Patients who have received prior therapy with any anti-vascular endothelial growth factor (VEGF) drug, including bevacizumab * Patients with clinical symptoms or signs of gastrointestinal obstruction and who require parenteral hydration and/or nutrition * 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 should feel free to consult the Study Chair or Study Co-Chairs for uncertainty in this regard * Patients with significant peripheral vascular disease * Patients with pre-existing grade 2 or greater peripheral neuropathy