This phase I trial is studying the side effects and best dose of adjuvant intraperitoneal carboplatin when given together with paclitaxel and bevacizumab in treating patients who have undergone debulking surgery for stage II , stage III, or stage IV ovarian epithelial, primary peritoneal, or fallopian tube cancer. Drugs used in chemotherapy, such as carboplatin and paclitaxel, work in different ways to stop tumor cells from dividing so they stop growing or die. Monoclonal antibodies, such as bevacizumab, can block tumor growth in different ways. Some block the ability of tumor cells to grow and spread. Others find tumor cells and help kill them or carry tumor-killing substances to them. Bevacizumab may also stop the growth of tumor cells by blocking blood flow to the tumor. It is not yet known whether carboplatin, paclitaxel, and bevacizumab are more effective than carboplatin and paclitaxel in treating ovarian epithelial or primary peritoneal cancer, or fallopian tube cancer.