Bedford played college football at the University of Texas at Austin where he was a four-year letterman and starter at cornerback as well as the defensive captain. He was a two-time All-Southwest Conference second team selection. He played in two Cotton Bowls and two Sun Bowls.[3] He set a then-Longhorn season record for pass breakups with 22 in 1981 and is currently in the top ten on UT's career pass breakup list (47). At the end of his senior year, he was named a Defensive Valuable Player in the 1982 Senior Bowl All-Star Game. He returned to Texas to receive his diploma in 1984.
Professional playing career
Bedford was selected in the fifth round of the 1982 NFL draft by the St. Louis Cardinals. He played one season for the Cardinals, spending most of it on the injured reserve list with a knee injury and was active for just two regular season games and one playoff game and recorded no stats.[4] After sitting out the 1983 season, he moved to the United States Football League (USFL), where he played one game each for the San Antonio Gunslingers and the Oklahoma Outlaws, again missing games with injuries. At the end of 1984 he was drafted by the Arizona Outlaws in the allocation draft, but never played for them.[5]