Bradford was born in Jackson, Mississippi. His father had suffered a stroke that left him partially paralyzed, so that he could only throw underhand when playing catch with his son. Author Michael Lewis speculates that memories of his father's throwing motion may have contributed to the development of Bradford's unusual underhand pitching style.
He attended Byram High School in Jackson. Unlike most players who become major leaguers, he had not exhibited outstanding athletic talent through the early years of high school. But his high school coach suggested he try sidearm pitching after learning some tips about the approach from a professional player. This technique brought him enough success to get a spot on the teams of Hinds Community College and the University of Southern Mississippi. He was drafted by the Chicago White Sox in 1994 but elected to stay in college through 1996. The White Sox - the only major league team that had even scouted him - re-drafted him in the 13th round of the 1996 MLB Draft. Quickly burning through the minor leagues, he made his major league debut in 1998 while only 23 years old.
In 1999, Bradford made only a short stop in the majors with the rest of the season spent with the triple-A Charlotte Knights. He was impressive again as a September call-up in 2000 and even pitched in the American League Division Series but the White Sox' bullpen was still full so they traded him to Oakland for catcher Miguel Olivo. Bradford spent most of the 2001 season with Oakland due to his microscopic 0.38 ERA with the triple-A Sacramento River Cats. It was his last regular stint in the minors.
From 2002 to 2004, Bradford was a specialty reliever for the A's, consistently baffling right-handed hitters but getting hit by left-handed hitters. His ERA stayed around 3.00 for his entire career until 2004 when mounting back pain forced him on to the disabled list.
Bradford is a submarine pitcher whose unorthodox delivery has caused him repeated back problems. He was a dependable setup man during four consecutive playoff appearances from 2000 to 2003, when he went 14-7 with five saves and a 2.92 ERA in 194 relief appearances. He has not allowed a run over his five different postseasons spanning three teams and nearly ten innings.
In July 2005, the Boston Red Sox acquired Bradford from Oakland in a trade for outfielder Jay Payton. Bradford, on the disabled list since undergoing lower back surgery March 7, was activated after the All-Star break. Bradford had mixed results in Boston, posting a 3.86 ERA in with a 1.414 WHIP, although he only pitched 23.3 innings. After the season, he became a free agent and was signed by the Mets where he was reunited with Rick Peterson, his pitching coach from the Athletics. He had a very solid year in 2006 as a right-handed specialist out of the bullpen, posting a 2.90 ERA in 70 games.
On November 28, 2006, Bradford signed a three-year contract with the Baltimore Orioles worth $10.5 million.
In 17 career postseason games, Bradford has posted a 0.00 ERA.
Moment in the Sun
- Had a chapter devoted to him in Moneyball.
On the origins of his submarine delivery: "I had a coach in high school that dropped me down. He dropped me down from over the top, and over the years, I've gotten lower and lower. I can't really go any further down from where I am, so I guess I've got to stop there. It started when I was 15 years old, really, and over the years it's changed." 
- June 4, 1996: Drafted by the Chicago White Sox in the 13th round of the 1996 amateur draft. Player signed June 6, 1996.
- December 7, 2000: Traded by the Chicago White Sox to the Oakland Athletics for Miguel Olivo.
- July 13, 2005: Traded by the Oakland Athletics to the Boston Red Sox for Jay Payton and cash.
- December 21, 2005: Granted Free Agency.
- December 27, 2005: Signed as a Free Agent with the New York Mets.
- November 28, 2006: Signed as a Free Agent with the Baltimore Orioles.