Anderson played at Washington from 1958 to 1963. He was selected by the team as Rookie of the Year in 1958 and player of the year in 1959. Bill made 178 catches, averaging 17.1 yards per catch, and scored 14 touchdowns over six seasons. Bill was a 2 time Pro-Bowl selection (1959 and 1960).
Bill retired from football in 1963 and joined the Tennessee staff as an assistant coach. Bill put his retirement plans on hold and signed with the Green Bay Packers in 1965. He played 24 games with Green Bay from 1965–1966 and averaged 11.9 yards per catch. The comeback was a good thing for Bill as he earned a Super Bowl ring when the Packers defeated the Kansas City Chiefs to win Super Bowl I on January 15, 1967.
For 31 seasons Anderson served as a color analyst on radio broadcasts of Tennessee football games, teaming with play-by-play announcer John Ward to form the longest-running broadcast partnership in college football.