After graduating with a Bachelor of Science degree in 1960, he decided to seek a career in theater, starting in New York City in improv with a troupe called The Premise.

After compulsory service as a draftee in the United States Army, he worked with an improv troupe in San Francisco known as The Committee, whose members included Rob Reiner, David Ogden Stiers, Howard Hesseman and Hamilton Camp.

In 1971, Bonerz was part of an ensemble cast in the short-lived improvisational television show Story Theatre, which also included Alan Alda and Valerie Harper.

In 1972, he landed the popular supporting role of Dr. Jerry Robinson, the eccentric orthodontist on The Bob Newhart Show, whose most frequent comic foil was Marcia Wallace as Carol, the sharp-tongued receptionist.

In 1986, Bonerz co-starred with Tuesday Weld and River Phoenix in the television movie Circle of Violence: A Family Drama.