Burdette was the leading scorer in the Mississippi Valley Conference as a freshman at UT Martin in 1935 when the school was UT Junior College. He was named to the all-conference team that year before transferring to Murray State where the teams he played on compiled a 72-9 record from 1936 to 1938. He led Murray State in scoring each of those years.
From 1946 to 1952, Burdette was the head basketball coach at the University of Alabama where his teams were seeded in the Southeastern Conference Tournament five of the six years. At Alabama he compiled a coaching record of 83-57. Burdette was named to the Tennessee Sports Hall of Fame in 1981; the Murray State Hall of Fame in 1967, and was awarded "The Volunteer" by UT Martin and the Award of Merit by the National Association of Basketball Coaches in 1971.