Inclusion Criteria:

- Histologically confirmed transitional cell carcinoma (TCC) of the urothelium

- Must have predominance of transitional histology, but foci of squamous and/or
adenocarcinoma histology allowed

- Poorly differentiated transitional cell carcinoma allowed

- TCC of any of the following sites allowed:

- Bladder

- Renal pelvis

- Ureter

- Urethra

- Measurable disease, defined as >= 1 unidimensionally measurable lesion >= 20 mm by
conventional techniques OR >= 10 mm by spiral CT scan

- Locoregionally advanced or metastatic disease that is not amenable to curative
surgery and/or radiotherapy

- Must have received 1 prior systemic chemotherapy regimen containing a platinum
compound (e.g., cisplatin, carboplatin, or oxaliplatin) in the neoadjuvant, adjuvant,
or metastatic setting

- No evidence of CNS disease, including primary brain tumor or brain metastases

- ECOG performance status 0-2

- Absolute neutrophil count >= 1,000/mm^3

- Platelet count >= 75,000/mm^3

- Bilirubin =< 1.5 times upper limit of normal (ULN)

- AST or ALT =< 2.5 times ULN

- Creatinine =< 2.5 times ULN OR creatinine clearance => 40 mL/min

- Urine protein: creatinine ratio =< 1 OR 24-hour urine protein < 500 mg

- INR =< 1.5 (unless on full-dose warfarin)

- Not pregnant or nursing

- Negative pregnancy test

- Fertile patients must use effective contraception during and for >= 6 months after
completion of study treatment

- No known hypersensitivity to Chinese hamster ovary cell products or other recombinant
human antibodies

- No history of allergic reactions attributed to compounds of similar chemical or
biological composition to other agents used in the study

- No serious or nonhealing wound, ulcer, or bone fracture

- No abdominal fistula, gastrointestinal perforation, or intra-abdominal abscess within
the past 28 days

- No significant traumatic injury within the past 28 days

- No clinically significant cardiovascular disease, including any of the following:

- Myocardial infarction, coronary artery bypass graft, or unstable angina pectoris
within the past 6 months

- New York Heart Association class III or IV congestive heart failure

- Serious cardiac arrhythmia requiring medication

- Clinically significant peripheral vascular disease within the past 6 months

- Cerebrovascular accident within the past 6 months

- Pulmonary embolism, deep vein thrombosis, or other thromboembolic event within
the past 6 months

- Uncontrolled hypertension, defined as blood pressure (BP) > 150/100 mm Hg or
systolic BP > 180 mm Hg (if diastolic BP < 90 mm Hg) within the past 3 months

- No evidence of bleeding diathesis or coagulopathy

- No uncontrolled intercurrent illness, including, but not limited to, any of the
following:

- Ongoing or active infection

- Psychiatric illness or social situation that would preclude study compliance

- Recovered from prior therapy

- Prior biologic or targeted therapies allowed

- No more than 1 prior systemic chemotherapy regimen for metastatic disease

- No prior antiangiogenic therapy primarily targeting the vascular endothelial growth
factor pathway

- At least 4 weeks since prior radiotherapy or systemic therapy (6 weeks for mitomycin
C or nitrosoureas)

- More than 28 days since prior major surgery or open biopsy

- More than 7 days since prior core biopsy

- No concurrent major surgery

- Concurrent full-dose anticoagulants (e.g., warfarin) allowed provided all of the
following criteria are met:

- In-range INR (usually between 2 and 3) on a stable dose of oral anticoagulant or
low molecular weight heparin

- No active bleeding or pathological condition that carries a high risk of
bleeding (e.g., tumor involving major vessels or known varices)

- No other concurrent investigational agents

- No concurrent combination antiretroviral therapy for HIV-positive patients