He played as a safety, punter and return specialist in the National Football League (NFL), earning All-Pro honors twice.

[1] His football talents, including the reputed ability to pass with either hand, earned him the nickname "Super Bill.

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.

In 1968, Texas started the season ranked #5 and introduced the wishbone formation on offense, with co-captain Bradley at quarterback.

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 would later recount that during his years with the Eagles, he would spend nights out on dates with members of the Philadelphia Phillies usherettes.

Bradley went into retirement, working in his family's restaurant in Palestine, but in November of that year he was signed by the St. Louis Cardinals when Mike Sensibaugh broke his leg.

He had been asked to come back by other teams – including Houston, Oakland and Pittsburgh,[3] but only accepted with St. Louis because they looked to be playoff-bound.

He had invested in a sports management company based in Philadelphia, but sold his shares in 1980 and went back to Palestine where he bought a farm and ran a gas station he owned.

From 1998 to 2000, he served as defensive backs coach for Wade Phillips, Ted Cottrell and the Buffalo Bills before moving to the same position with the New York Jets from 2001 to 2003.

Bradley returned to college coaching when his former Eagle teammate Guy Morriss hired him to be defensive coordinator for 2004–2006 at Baylor University.

He then returned to the NFL to reunite with Defensive Coordinator Ted Cottrell as the San Diego Chargers secondary coach from 2006 to 2008.

[9] He retired from Lamar, and from coaching, in 2014, in part to help take care of his stepson who had suffered brain trauma as the result of a violent attack.

[2] In 2019, Bradley was the defensive backs coach of the San Antonio Commanders of the AAF until the league went bankrupt.