Bradford was born in Tyler, Texas, the son of Rose and Richard Edwin Bradford. His stepfather was a wholesale grocer. He first studied acting at the Actors' Studio in New York. As well as his numerous TV appearances, Bradford has featured in many films, such as The Chase (1966), More American Graffiti (1979), and The Legend of Billie Jean (1985), and The Trip To Bountiful (1986), but his best known role in the cinema was in Brian De Palma's The Untouchables (1987), playing corrupt Irish cop Mike Dorsett, and also having a notable fight scene with Sean Connery. Bradford played a similar police officer in the 1997 film Hoodlum featuring Laurence Fishburne, Andy García, and Tim Roth. Bradford appeared in the 1989 film Heart of Dixie.
He also guest starred NBC's "Viper (TV series)"
He appeared in one episode of the Television series Gunsmoke in the 1960s.
He was also a semi-regular cast member of the television crime series Cagney & Lacey. In 2004 Richard Bradford gave a series of interviews and commentaries for a DVD release of Man in a Suitcase, expressing mild surprise at the ongoing popularity of the series today.
Bradford married ballet dancer Eileen Elliott.
In 1986 The Smiths used a photograph of Bradford on the cover of their single "Panic".