[1] Bramley made his film debut in the Academy Award-winning 1961 movie musical West Side Story,[2] co-directed by Robert Wise and co-starring Richard Beymer.

Other film credits include Gunpoint (1966), I Love You, Alice B. Toklas (1968), Getting Straight (1970), Suppose They Gave a War and Nobody Came?

(1970), Doctors' Wives (1971), Bless the Beasts & Children (1971), Hangup (1974), Revenge of the Cheerleaders (1976), and The Wild Life (1984).

He appeared in TV movies including Ready for the People (1964), Trial Run (1969), Michael O'Hara the Fourth (1972), The Last Day (1975), Tough Girl (1981).

Bramley made guest appearances on such TV series as Gunsmoke, Bonanza, Combat!, Straightaway, Kentucky Jones, Lassie (1969 episode "Patsy"),The Virginian, Bewitched, I Dream of Jeannie (as a policeman), Emergency!, McCloud, Gomer Pyle, and Barnaby Jones.