This phase I trial studies the side effects and best dose of paclitaxel albumin-stabilized nanoparticle formulation and bevacizumab in treating patients with stage IV melanoma that cannot be removed by surgery or with cancer of the cervix, endometrium, ovary, fallopian tube or peritoneal cavity. Drugs used in chemotherapy, such as paclitaxel albumin-stabilized nanoparticle formulation, 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 block tumor growth in different ways by targeting certain cells. Giving paclitaxel albumin-stabilized nanoparticle formulation and bevacizumab may kill more tumor cells.