Bradley entered the
University of Texas at Austin in 1965 and became the
starting quarterback and punter in 1966 as a sophomore. In 1966, he led the Longhorns to a 7–4 record and a victory over Mississippi in the Bluebonnet Bowl. Injured during a win over
Indiana, he sat out the Oklahoma game in favor of back-up Andy White, and
Oklahoma notched its first win in the rivalry since 1957. Bradley came back the following week and finished the season as the
Southwest Conference's leader for rushing touchdowns with 6. In the Bluebonnet Bowl, Bradley and running back
Chris Gilbert each ran for over 100 yards, marking the first time that two Longhorns had run for over 100 yards in the same bowl game. Bradley was starting quarterback again the next season. Texas started the season ranked #5, but back-to-back losses to #4 USC and Texas Tech knocked them from the rankings. They then ran off 6 straight wins before ending the season with another pair of back-to-back losses, this time to TCU and Texas A&M to finish 6-4 and missing out on a bowl game. Despite the down year, Bradley led the Southwest Conference in total touchdowns with 14. In 1968, Texas started the season ranked #5 and introduced the
wishbone formation on offense, with co-captain Bradley at quarterback. Struggling with the new offense, Texas with Bradley under center tied #11 Houston and lost to Texas Tech.
James Street replaced Bradley during the 3rd quarter of the Texas Tech game and never relinquished the position, leading the Longhorns to 9 consecutive wins, a Southwest Conference Championship and victory in the Cotton Bowl. Bradley was moved to
wide receiver for two weeks, and then to defensive back and kick-off returner. As a defensive back he set the Texas and Southwest Conference records for most interceptions in a game when he picked off
Texas A&M four times at the end of the regular season. His final game as a Longhorn was the 36–13 win over Tennessee in the Cotton Bowl. He then played in the 1969
Hula Bowl, the Coaches All-America Game and the
College All-Star Game.
Records • UT – Most passing yards, game (220 yards), broke his own record set earlier that year, surpassed by
Rick McIvor in 1979 •
UT – Longest punt, bowl game (74 yards) • UT – Most Offensive Yards, season (1,624), surpassed by
Earl Campbell in 1977 •
Southwest Conference and UT – Most interceptions caught, game (4) Bold means still active ==NFL career==