Bonner was born in Little Rock, Arkansas, the son of Mamie Grace (née Dobbins), a singer, and Frank Woodrow Boers, a saxophone player. Bonner started his acting career in the experimental 1967 independent film The Equinox ... A Journey into the Unknown, which was remade as the 1970 cult classic Equinox (credited as Frank Boers, Jr.).
Bonner appeared as a guest star in one episode of the sitcom Night Court in the 1980s. From 1988 to 1990, Bonner played the role of Father Hargis, headmaster of the fictional St. Augustine's Academy on the TV show Just the Ten of Us which was a spin-off of Growing Pains. Bonner also appeared in one of the early episodes of the television show Newhart.
He reprised the role of Herb Tarlek in the 1991 spinoff The New WKRP in Cincinnati, and in a 2004 rock video for Canadian indie rock band Rheostatics (for the song "The Tarleks", from their album 2067).
