Bradford was born in Tyler, Texas, the son of Rose and Richard Edwin Bradford. His stepfather was a wholesale grocer. Raised by his grandparents in Conroe, Bradford received his schooling in San Antonio, before attending Texas A&M on a football scholarship.
When an injury short-circuited Bradford's budding athletic career, and a subsequent switch to baseball at Texas State University was stymied due to insufficient semester hours, Bradford finally decided to seriously pursue a long-contemplated career in acting. To this end he made his way to New York.
Supporting himself by waiting tables, Bradford studied acting, first with Frank Corsaro, and finally, in 1962, was admitted to the Actors Studio, where he worked for two years, leading to roles in Studio productions such as Mother Courage (1963), June Havoc's Marathon '33 (1963), and Blues for Mister Charlie (1964). Also, he understudied Rod Steiger in the touring production of A.E. Hotchner's Hemingway-based A Short, Happy Life (1961), an ostensibly Broadway-bound show which folded out of town.
Eventually, Bradford's work caught the eye of another Actors Studio member, director Arthur Penn, who cast Bradford in The Chase (1966), where he held his own alongside Janice Rule, Martha Hyer and a host of Studio veterans, including Marlon and Jocelyn Brando, E.G. Marshall, and Clifton James, as well as newcomers Jane Fonda and Robert Redford and future member Robert Duvall. This work, in turn, attracted the attention of media impresario Lew Grade, who would bring Bradford to Great Britain in 1967 for Man in a Suitcase.
In addition to his numerous TV appearances, Bradford has been featured in many films, such as The Missouri Breaks (1976), An Enemy of the People (1978), Badge of the Assassin (1985), The Trip To Bountiful (1985), The Untouchables (1987) and The Milagro Beanfield War (1988), but arguably his best known film role is the corrupt police captain in the 1997 film Hoodlum featuring Laurence Fishburne, Andy García, and Tim Roth. Bradford also appeared in the 1989 film Heart of Dixie, and had notable turns in Costa-Gavras' Missing (1982), the Kurt Russell thriller The Mean Season (1985) and was also in The Crossing Guard (1995) with Jack Nicholson.
He also guest starred on NBC's Viper. In 1987 he starred in the miniseries Amerika.
In the 1960s, he appeared in one episode of the Television series Gunsmoke and guest starred in an episode of the TV western series The High Chaparral. In the 1970s, he played Lutie Bascomb in one episode of The Waltons. He guest starred in an episode of Murder, She Wrote in the 1980s.
In the mid 1980s he was also a semi-regular cast member of the television police 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.
He was subsequently in a long-time relationship with actress Millie Perkins, with whom he had two stepchildren. He also had one son.
In 1986 The Smiths used a photograph of Bradford on the cover of their single "Panic". He died on March 22, 2016.