Bevacizumab and Erlotinib in Treating Patients With Recurrent or Metastatic Ovarian Epithelial, Fallopian Tube, or Primary Peritoneal Cavity Cancer

Inclusion Criteria: * Histologically or cytologically confirmed ovarian epithelial, fallopian tube, or primary peritoneal cavity cancer * Recurrent or metastatic disease * Measurable disease, defined as ≥ 1 unidimensionally measurable indicator lesion ≥ 20 mm by conventional techniques OR ≥ 10 mm by spiral CT scan * Must have received a platinum-containing chemotherapy regimen for primary disease * Re-treatment with a platinum-based regimen required for patients who achieved a clinical complete response (CR) to primary therapy and then had a treatment-free interval \> 12 months (i.e., platinum-sensitive) unless the patient developed a hypersensitivity to platinum * Patients with a treatment-free interval \< 12 months do not require prior chemotherapy for recurrent disease * No evidence of CNS disease, including primary brain tumors or brain metastasis * Performance status - ECOG 0-2 * More than 3 months * WBC ≥ 3,000/mm\^3 * Absolute neutrophil count ≥ 1,500/mm\^3 * Platelet count ≥ 100,000/mm\^3 * No history of bleeding diathesis * SGOT and SGPT ≤ 2.5 times upper limit of normal (ULN) (5 times ULN if due to liver metastasis) * Bilirubin normal * INR ≤ 1.5 (3 if receiving warfarin) * No history of esophageal varices * Creatinine ≤ 1.5 mg/dL * Creatinine clearance ≥ 60 mL/min * Urine protein \< 1+ * Urine protein \< 1,000 mg on 24-hour urine collection * Urine protein:creatinine ratio \< 1.0 * No arterial thromboembolic event within the past 6 months, including any of the following: * Transient ischemic attack * Cerebrovascular accident * Unstable angina pectoris * Myocardial infarction * No clinically significant peripheral artery disease * No uncontrolled hypertension * No New York Heart Association grade II-IV congestive heart failure * No serious cardiac arrhythmia requiring medication * No peripheral vascular disease ≥ grade 2 * Not pregnant * No nursing during and for ≥ 3 months after study participation * Negative pregnancy test * Fertile patients must use effective contraception during and for ≥ 3 months after study participation * No history of allergic reaction attributed to compounds of similar chemical or biological composition to study drugs (e.g., Chinese hamster ovary cell products or recombinant humanized antibodies) * No serious or non-healing wound, ulcer, or bone fracture * No active infection requiring parenteral antibiotics * No other active malignancy within the past 5 years except nonmelanoma skin cancer or carcinoma in situ of the cervix * No gastrointestinal tract disease resulting in an inability to take oral medication * No significant traumatic injury within the past 28 days * No known HIV positivity * No prior bevacizumab * See Disease Characteristics * No more than 2 prior cytotoxic chemotherapy regimens for recurrent or refractory disease (i.e., failed to achieve a clinical CR after primary therapy) * More than 4 weeks since prior chemotherapy (6 weeks for nitrosoureas or mitomycin) * More than 4 weeks since prior radiotherapy * No prior radiotherapy to any indicator lesion unless disease has progressed since completion of radiotherapy * More than 4 weeks since prior major surgical procedure or open biopsy * More than 1 week since prior core biopsy * No prior surgery affecting absorption * No concurrent major surgery * Recovered from prior therapy * No prior vascular endothelial growth factor (VEGF) or an epidermal growth factor receptor (EGFR) directed therapy * No prior erlotinib * At least 30 days since prior investigational drugs * More than 1 month since prior thrombolytic agents * Concurrent warfarin allowed provided the following criteria are met: * Patient is on a therapeutic stable dose of warfarin * INR ≤ 3 * No active bleeding or pathological condition that would confer a high risk of bleeding (e.g., tumor invading adjacent organs or major blood vessels or varices that are likely to bleed) * No other concurrent investigational agents * No other concurrent anticancer therapy