 This randomized phase III trial studies chemotherapy to see how well it works with or without bevacizumab in treating patients with head and neck squamous cell carcinoma that has come back recurrent or that has spread to other parts of the body metastatic. Drugs used in chemotherapy, such as docetaxel, cisplatin, carboplatin, and fluorouracil, 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. Bevacizumab may also make tumor cells more sensitive to chemotherapy and stop the growth of head and neck cancer by blocking blood flow to the tumor. It is not yet known whether combination chemotherapy is more effective when given with or without bevacizumab in treating patients with head and neck squamous cell carcinoma. 