While many of his characters appear to be swamp people, Bill actually comes from an upper-class family with a strong connection to Yale University. He is the son of Virginia Gillette (Kleitz) and S. D. Moseley (Spencer Dumaresq Moseley). His mother was a journalist. His father was a captain and center of the 1942 Yale football team, a member of the Yale Corporation, and chairman and chief executive of the Railway Express Agency. Bill's paternal grandfather, George Moseley, was also a Yale football star. His maternal grandfather, William Lambert Kleitz, was a president and director of Guaranty Trust Co.