Bradley graduated from Hartwick College in 1934, where he was a member of Phi Sigma Kappa fraternity.

Bradley coached Duke Blue Devils men's basketball legend Dick Groat during his nine-year tenure with the Blue Devils, which spanned from 1950 to 1959 and resulted in Duke's first NCAA tournament appearances.

Bradley was hired as the Texas Longhorns men's basketball coach in 1959 and led the Longhorns to two NCAA Tournaments as a result of winning the Southwest Conference outright twice in eight years.

Bradley's 1960 and 1963 Longhorns teams made the Sweet 16 of the NCAA Division I men's basketball tournament.

Conference tournament champion # denotes interim head coach