 This randomized phase III trial is to see if combining erlotinib with bevacizumab works better in treating patients who have recurrent or metastatic head and neck cancer. Erlotinib may stop the growth of tumor cells by blocking the enzymes needed for tumor cell growth. Monoclonal antibodies, such as bevacizumab, can block cancer growth in different ways. Some block the ability of cancer cells to grow and spread. Others find cancer cells and help kill them or deliver cancer-killing substances to them. Combining erlotinib with bevacizumab may kill more tumor cells. 