Bramley made his film debut in the Academy Award-winning 1961 movie musical West Side Story, co-directed by Robert Wise and co-starring Richard Beymer. Bramley played the role of policeman Officer Krupke. He also appeared in the 1968 film Madigan. 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).