Cisplatin, Bevacizumab, and Gemcitabine Followed by Surgery, Bevacizumab, and Paclitaxel in Treating Patients With Locally Advanced Nonmetastatic Bladder Cancer That Can Be Removed By Surgery

DISEASE CHARACTERISTICS: * Histologically confirmed transitional cell cancer (TCC) of the bladder * Staged as follows: * Muscle invasive (T2-T4a) * Node negative (N0) * No histologically or cytologically proven lymph node metastases * Nonmetastatic (M0) * No evidence of distant metastases * Resectable disease * Able to begin protocol treatment within 6 weeks after transurethral resection and cystoscopic evaluation * No central nervous system or brain metastases PATIENT CHARACTERISTICS: * ECOG performance status of 0-2 * Karnofsky 60-100% * White blood cell count ≥ 3,000/mm\^3 * Absolute neutrophil count ≥ 1,500/mm\^3 * Platelet count ≥ 100,000/mm\^3 * AST(SGOT) and ALT(SGPT) ≤ 2 times upper limit of normal * Bilirubin ≤1.5 mg/dL * Creatinine clearance ≥ 60 mL/min * Urine protein/creatinine ratio \< 1.0 * Blood pressure ≤150/100 mm Hg * No prohibitive medical risks for chemotherapy * No history of allergic reactions attributed to compounds of similar chemical or biologic composition to cisplatin, gemcitabine hydrochloride, or paclitaxel * No unstable angina * No history of myocardial infarction within the past 6 months * No cardiac arrhythmias * No New York Heart Association (NYHA) congestive heart failure ≥ grade 2 * No history of stroke within the past 6 months * No clinically significant peripheral vascular disease * No evidence of bleeding diathesis or coagulopathy * No history of abdominal fistula, gastrointestinal perforation, or intra-abdominal abscess within the past 6 months * No serious nonhealing wound, ulcer, or bone fracture * No psychiatric illness or other psychosocial situation that would limit ability to comply with study and/or follow-up procedures * Not pregnant or nursing * Negative pregnancy test * Fertile patients must agree to use adequate contraception prior to study entry and for the duration of study participation * No significant traumatic injury with in the past 28 days PRIOR CONCURRENT THERAPY: * No prior systemic chemotherapy * No prior pelvic radiation therapy * More than 4 weeks since prior participation in an experimental drug study other than a Genentech-sponsored bevacizumab cancer study * No concurrent participation in an experimental drug study other than a Genentech-sponsored bevacizumab cancer study * No major surgical procedure or open biopsy within the past 28 days * No anticipation of need for major surgical procedure during the course of the study * No minor surgical procedures, fine-needle aspirations, or core biopsies within the past 7 days * No concurrent treatment with hormones or other chemotherapeutic agents except the following: * Steroids given for adrenal failure * Hormones administered for nondisease-related conditions (e.g., insulin for diabetes) * Intermittent use of dexamethasone as an antiemetic in solid tumor protocols * No other concurrent investigational or commercial agents or therapies