After his sophomore season at Kentucky, Bradley transferred to Villanova University where he started. That season he averaged 20.8 points per game and 9.8 rebounds per game.
Even though he had one year of college eligibility remaining, Bradley left school to go to the NBA in 2001 and was selected as the 17th pick in the 1st round of the NBA Draft by the Toronto Raptors. During his rookie season, Bradley averaged 1.2 points per game and 0.9 rebounds per game.
His statistics improved in 2002-03 (5 ppg and 6 rpg in 20 minutes), but in the following season was sidelined constantly for a bruised right clavicle. He was let go by the Raptors in March 2004, and would later be signed by the Atlanta Hawks. In 2004-05 he started off with the Orlando Magic, but was traded twice during that season, to the Sacramento Kings and the Philadelphia 76ers. Played 46 games with the Sixers in 2005-06, his best in two years, mainly because of constant injuries to Chris Webber.
In the 2006-07 season he signed for Bruesa GBC in the Spanish ACB. After spending one season with the Spanish team, Bradley moved to Germany and signed with ALBA Berlin in August but was released in November. He did not stay unemployed for long, signing with Lithuanian power Žalgiris on November 15. However, he was limited by injuries, averaging only 7 points and 4.9 rebounds in seven games, and became expendable when Žalgiris signed Mamadou N'Diaye in February 2008. Bradley was waived on February 12, 2008.