This phase I/II trial is studying the side effects and best dose of vorinostat when given together with paclitaxel and bevacizumab and to see how well they work in treating patients with metastatic breast cancer and/or breast cancer that has recurred in the chest wall and cannot be removed by surgery. Vorinostat may stop the growth of tumor cells by blocking some of the enzymes needed for cell growth. Drugs used in chemotherapy, such as paclitaxel, work in different ways to stop the growth of tumor cells, either by killing the cells or by stopping them from dividing. Monoclonal antibodies, such as bevacizumab, can block tumor growth in different ways. Some find tumor cells and kill them or carry tumor-killing substances to them. Others interfere with the ability of tumor cells to grow and spread. Bevacizumab may also stop the growth of tumor cells by blocking blood flow to the tumor. Giving vorinostat together with paclitaxel and bevacizumab may kill more tumor cells.