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 pitching style. 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.