Burmester appeared with the Actor's Theatre of Louisville, originating roles in the plays "Getting Our" and "Lone Star", and eventually recreating them in his Off-Broadway and Broadway debuts, respectively. He made his feature film debut in "House of God" (1979), but first worked 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). Yet, even after further Broadway success in "Big River" (1981), he was playing small roles in films. He was Holly Hunter's father in the prologue "youth backstory" sequence in "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), in which Burmester was Catfish DeVries, decompression expert.
TV has provided wider employment. Burmester first broke into regular TV series work as the dimwitted mechanic, Randy, on the "Alice" spin-off "Flo" on CBS from 1980-1981, and he made an auspicious debut in miniseries playing Eban Krutch in "George Washington" (CBS, 1984), a role he reprised for "George Washington II: The Forging of a Nation" (CBS, 1986). In 1989, Burmester was a regular on the short-lived NBC series "True Blue" playing Red, the southern good ol' boy working with the NYPD emergency service unit. He had a shot as a series lead in "Arresting Behavior" (ABC, 1992), playing Officer Bill Ruskin of Vista Valley. Returning to miniseries and TV movies, Burmester was the plantation overseer in "Queen" (CBS, 1993), and Frank Vassar in "Truman" (HBO, 1995). His size played in his role as the plump convict in "William Faulkner's Old Man" (CBS, 1997). During the 1997-1998 season he was set to play the father of a young woman who marries a Jewish man in "You're the One," a midseason entry for the WB (a.k.a. "Us and Them").