Burmester worked for director John Sayles several times, including in Passion Fish (1992) and Lone Star (1996), and also for directors such as John Schlesinger and Sidney Lumet, and as the Apostle Nathaniel in Martin Scorsese's The Last Temptation of Christ (1988).
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 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.