"Bruno" was 'Bruce Willis (I)''s nickname from his bartending days.
In the "Cavern"-like sequence, shot at the Whiskey in L.A., Bruno/Bruce is played by his brother, David Willis, wearing a John Lennon type of hat. He was a P.A. on the production and was pressed into service when Bruce failed to show because he was still in Hawaii.
Bruce Willis "lip-synced" the harmonica in the Peter Gunn performance in the section showing Bruno with his band, "Bruno and The Bassment", a band with six bass players. The harmonica was actually played by Willis' friend, Bruce DiMattia. In fact, DiMattia played all of the harmonica heard throughout the dramatic part of the movie with Willis doing his own harmonica work only during the live concert at the end of the show.