This randomized phase III trial studies gemcitabine hydrochloride, cisplatin, and bevacizumab to see how well they work compared with gemcitabine hydrochloride and cisplatin in treating patients with urinary tract cancer that has spread to other places in the body. Drugs used in chemotherapy, such as gemcitabine hydrochloride and cisplatin, work in different ways to stop the growth of tumor cells, either by killing the cells, by stopping them from dividing, or by stopping them from spreading. Monoclonal antibodies, such as bevacizumab, may interfere with the ability of tumor cells to grow and spread. It is not yet known whether gemcitabine hydrochloride and cisplatin are more effective when given with or without bevacizumab in treating patients with urinary tract cancer.