DISEASE CHARACTERISTICS: - Histologically confirmed transitional cell carcinoma of the urinary tract (renal pelvis, ureter, bladder, prostate, or urethra) - Unresectable or progressive metastatic or locally advanced disease (T4b, N2, N3 or M1) - Not a candidate for potentially curative surgery or radiotherapy - No history of peritoneal carcinomatosis - No known brain metastases PATIENT CHARACTERISTICS: - ECOG performance status (PS) 0-1 OR Karnofsky PS 80-100% - ANC ≥ 1,500/mm^3 - Platelet count ≥ 100,000/mm^3 - Bilirubin ≤ 1.25 times upper limit of normal (ULN) (≤ 2.5 times ULN for patient's with Gilbert's disease) - AST ≤ 2.0 times ULN - Creatinine clearance ≥ 60 mL/min - Urine protein:creatinine ratio < 1.0 OR urine protein ≤ 1+ - Not pregnant or nursing - Negative pregnancy test - Fertile patients must use effective contraception during and for up to 3 months after completion of study treatment - No NYHA class II-IV congestive heart failure - History of hypertension allowed provided it is well controlled (i.e., BP < 150/90 mm Hg) on a regimen of anti-hypertensive therapy - No arterial thrombotic events within the past 6 months, including any of the following: - Transient ischemic attack - Cerebrovascular accident - Peripheral arterial thrombus - Unstable angina or angina requiring surgical or medical intervention - Myocardial infarction - No clinically significant peripheral artery disease (i.e., claudication on < one block) - Deep venous thrombosis or pulmonary embolus within the past 6 months allowed provided patient is on stable therapeutic anticoagulation - No significant bleeding events (e.g., hemoptysis, upper or lower gastrointestinal [GI] bleeding, or grade 3 or 4 gross hematuria uncontrolled by transurethral resection of the bladder tumor) within the past 6 months - No GI perforation within the past 12 months - No serious or non-healing wound, ulcer, or bone fracture - No sensory or motor peripheral neuropathy ≥ grade 2 - No known hypersensitivity to Chinese hamster ovary cell products or other recombinant human antibodies PRIOR CONCURRENT THERAPY: - At least 4 weeks since prior radiotherapy (including palliative radiotherapy) or major surgery and recovered - At least 4 weeks since prior intravesical therapy - No prior combination systemic chemotherapy for metastatic disease - Single-agent radiosensitizing chemotherapy is not considered prior systemic therapy - Prior neoadjuvant or adjuvant systemic chemotherapy allowed provided it was completed ≥ 1 year prior to the diagnosis of metastatic disease - No prior bevacizumab or other angiogenesis inhibitors - No concurrent radiotherapy (including palliative radiotherapy) - Concurrent full-dose anticoagulants allowed provided patient is on a stable dose of warfarin and has an in-range INR (between 2 and 3) OR is on a stable dose of low molecular weight heparin - Concurrent anti-platelet agents, daily prophylactic aspirin, or anticoagulation agents for atrial fibrillation allowed