Evaluation of Weekly Ixabepilone With or Without Biweekly Bevacizumab

Inclusion Criteria: * Patients must have platinum-resistant/refractory (i.e., platinum-free interval \<6 months) recurrent or persistent histologically confirmed epithelial (non-mucinous) ovarian, fallopian tube, or primary peritoneal cancer. Patients may have serous, endometrioid, clear cell, carcinosarcoma, or transitional cell/malignant Brenner, mixed, or undifferentiated histologies. * Patients must have specimen available for immunohistochemistry for class III β-tubulin status; recurrent tumor specimen is preferred, though this may be performed on primary tumor if no recurrent tumor is available. * All patients must have measurable disease. Measurable disease is defined as lesions that can be measured by physical examination or by means of medical imaging techniques. 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 or plain x-ray, or ≥ 10 mm when measured by spiral CT and/or MRI. Ascites and pleural effusions are not to be considered measurable disease. * Patients must have at least one "target lesion" to be used to assess response on this protocol as defined by RECIST v1.1 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. * At the time of initial surgery, patients may have been optimally (\<1 cm diameter residual disease) or sub-optimally (≥1 cm diameter of residual disease) debulked. * Patients with measurable recurrent disease of any previous stage (I-IV) are eligible to enrollment. * The diagnosis must be histologically confirmed by a gynecologic pathologist. * Patients must have adequate bone marrow, kidney, and liver function: 1. Absolute neutrophil count greater than or equal to 1500 cells/mm3 2. Platelets greater than or equal to 100,000/uL 3. Renal function: creatinine less than or equal to 2.0 mg/dL 4. Hepatic function: Bilirubin ≤ 1.5 X laboratory normal 5. SGOT/SGPT ≤ 3 X laboratory normal. * Patients must have an ECOG performance status of 0-2. * Patients must have signed an approved informed consent. * Patients must have recovered from effects of recent surgery, radiotherapy, or chemotherapy. They should be free of significant infection. * Patients must have received prior treatment with taxanes. There is no limit on the number of prior lines of therapy. * Patients may have received prior bevacizumab therapy alone or in combination with chemotherapy. A 3-week washout period is required. * Patients of childbearing potential must have a negative serum pregnancy test within 7 days prior to the study entry and be practicing an effective form of contraception (section 7.5.3). * Patients must be at least 18 years of age. Exclusion Criteria: * Patients with a history of other invasive malignancies, with the exception of non-melanoma skin cancers, are excluded if there is any evidence of other malignancy present within the last five years. Patients are also excluded if their previous cancer treatment contraindicates this protocol therapy. * Patients who have a significant history of cardiac disease, i.e., uncontrolled hypertension, unstable angina, uncontrolled congestive heart failure, or uncontrolled arrhythmias within 6 months of registration (NYHA classification III-IV). * Patients with any unstable medical issue (including cardiac issues as above, active treatment for symptomatic pulmonary embolism, CVA, renal or hepatic insufficiency, active infection/sepsis requiring intravenous antibiotics). In patients who have undergone surgery, 28 days should elapse before initiation and the surgical site should be adequately healed. * Known brain/leptomeningeal involvement of the disease, active neurological disease such as uncontrolled seizure disorder or moderate to severe dementia. * Patients who have received prior therapy with any covalent irreversible anti-angiogenic tyrosine kinase inhibitor (e.g., vandetanib). * Patients known to be seropositive for human immunodeficiency virus (HIV) and active hepatitis, even if liver function studies are in the eligible range. * Known hemorrhagic diathesis or active bleeding disorder, including platelet count \<100,000/uL, or inadequate granulocytes, including an absolute neutrophil count \<1500 cells/mm. * Any hypersensitivity to Cremophor® EL or polyoxyethylated castor oil. * CTCAE grade 2 or higher peripheral neuropathy.