Bunch first joined Sesame Workshop in 1993 as an ensemble puppeteer on Sesame Street. He has played hundreds of Anything Muppets and background characters over the years. He was one of the principal puppeteers on Bear in the Big Blue House, performing and voicing some of the main characters. He also composed several songs for the show.
Bunch joined the cast of Oobi in 1999 as one of the four original cast members. In an interview with the Newsweek magazine, Josh Selig mentioned that unlike the other puppeteers of Oobi, Bunch intentionally left his arm unshaved so that Grampu would have the appearance of an elderly grandfather. By comparison, the other cast members all had to shave their arms regularly because they played younger characters. However, Bunch still visited a manicurist to get his nails touched up every week during production.