Bates was born in Salem, Massachusetts, the son of Nora (Jennings) and Representative George J. Bates of the 6th Massachusetts Congressional District, who also served as Salem's mayor. He attended local schools and graduated from Worcester Academy in 1936. He received his undergraduate education at Brown University, Providence, R.I., graduating in 1940. Following graduation from Brown, he enlisted in the United States Navy in July 1940 and was commissioned as ensign in the Naval Reserve on January 30, 1941. Bates then received instruction at the Naval Reserve Supply Officer's School at the Naval Medical Center, Washington, D.C., before serving successive tours of duty at the Washington Navy Yard and in Constellation (IX-20).
He remained a naval reservist, and by 1949 had become the supply officer for the 4th Naval District. While Bates was stationed there, his father was killed in a plane crash at the Washington National Airport on November 1, 1949.
Bates died of stomach cancer on June 22, 1969.[8] Immediately upon his death, the U.S. Navy attack submarineUSS William H. Bates (SSN-680), originally planned to be named USS Redfish, was renamed in his honor before her construction began.