Bevacizumab in Treating Patients With Persistent or Recurrent Ovarian Epithelial Cancer or Primary Peritoneal Cancer

Inclusion Criteria: * Histologically confirmed ovarian epithelial or primary peritoneal carcinoma * Recurrent or persistent after initial standard surgery or chemotherapy * Incurable with standard surgery, chemotherapy, or radiotherapy * At least 1 unidimensionally measurable target lesion * At least 20 mm by conventional techniques * At least 10 mm by spiral CT scan * Outside the area of prior radiotherapy * Accessible to guided core needle biopsy * Received 1 prior platinum-based chemotherapy regimen (e.g., carboplatin, cisplatin, or another organoplatinum compound) for primary disease * May have included high-dose therapy, consolidation, or extended therapy administered after surgical or non-surgical assessment * Patients with only 1 prior platinum-based chemotherapy regimen must have an initial treatment-free interval of less than 12 months * Patients with an initial treatment-free interval of more than 12 months must have progressive disease after prior platinum-based chemotherapy regimen as second-line therapy * No tumors involving major blood vessels * No evidence of CNS disease (primary brain tumor or brain metastases) within the past 5 years * Ineligible for higher priority Gynecologic Oncology Group (GOG) protocols (i.e., active phase III GOG protocols for the same patient population) * Performance status - GOG 0-2 (patients who have received 1 prior regimen) * Performance status - GOG 0-1 (patients who have received 2 prior regimens) * Absolute neutrophil count ≥ 1,500/mm\^3 * Platelet count ≥ 100,000/mm\^3 * No known bleeding disorder or coagulopathy * No active bleeding * Bilirubin ≤ 1.5 times upper limit of normal (ULN) * serum glutamate oxaloacetate transaminase (SGOT) ≤ 2.5 times ULN * Alkaline phosphatase ≤ 2.5 times ULN * PT (INR) ≤ 1.5 (INR 2-3 if on stable dose of therapeutic warfarin or low molecular weight heparin) * Partial thromboplastin time (PTT) \< 1.2 times control * Creatinine ≤ 1.5 times ULN * Creatinine clearance \> 60 mL/min * No proteinuria, as indicated by 1 of the following: * Negative urine dipstick * Urine protein \< 30 mg/dL * Urine protein \< 1,000 mg on 24-hour urine collection * No clinically significant cardiovascular disease, including any of the following: * Uncontrolled hypertension * Myocardial infarction within the past 6 months * Unstable angina within the past 6 months * New York Heart Association class II-IV congestive heart failure * Serious cardiac arrhythmia requiring medication * Peripheral vascular disease ≥ grade 2 * No stroke within the past 5 years * No pathologic condition that carries a high risk of bleeding * No significant traumatic injury within the past 28 days * No other invasive malignancy within the past 5 years except nonmelanoma skin cancer * No uncontrolled seizures within the past 5 years * No neuropathy (motor and sensory) ≥ grade 2 * No serious non-healing wound, ulcer, or bone fracture * No known hypersensitivity to Chinese hamster ovary cell products or other recombinant human or humanized antibodies * No active infection requiring parenteral antibiotics * No known claustrophobia that would preclude MRI tolerance * No ferromagnetic implants or pacers * Not pregnant or nursing * Negative pregnancy test * Fertile patients must use effective contraception during and for at least 3 months after study treatment * At least 3 weeks since prior immunologic therapy directed at malignancy * No prior bevacizumab * No other concurrent immunotherapy directed at malignancy * One additional prior cytotoxic regimen for recurrent or persistent disease allowed * No prior non-cytotoxic chemotherapy for recurrent or persistent disease * No concurrent chemotherapy directed at malignancy * At least 1 week since prior hormonal therapy directed at malignancy * No concurrent hormonal therapy directed at malignancy * Concurrent hormone replacement therapy allowed * Recovered from prior radiotherapy * No concurrent radiotherapy directed at malignancy * At least 28 days since prior major surgery or open biopsy and recovered * At least 7 days since prior core biopsy or placement of vascular access device * No anticipated need for major surgical procedure during study participation * At least 3 weeks since other prior therapy directed at malignancy * No prior anticancer therapy that would preclude study entry