Burmester appeared with the Actors Theatre of Louisville, originating roles in the plays Getting Out and Lone Star, and eventually recreating them in his Off-Broadway and Broadway debuts, respectively. He made his feature film debut in a big budget project with Cruising (1980), and had a featured role as the mortuary Director in Honky Tonk Freeway (1981). Burmester played one of the FBI agents hounding the faux Rosenberg couple in Daniel (1983). He played the role of Thénardier in the Original Broadway production of Les Misérables and the Police Sergeant in Harry Connick, Jr.'s musical Thou Shalt not.
He played Holly Hunter's character's father in the prologue of Broadcast News (1987), and the bum in front of The Plaza in Big Business (1988). Roles started to get larger with James Cameron's The Abyss (1989), as Catfish DeVries, decompression expert.
Although thought to have died of leukemia, death was caused by a tick bite that was complicated by his compromised immune system. He died at age 63 on June 28, 2007. His ashes were scattered in Kentucky.
