Although Bob Burnet never became famous himself, he was well featured as the trumpet soloist with the Charlie Barnet Orchestra during a period when Barnet was starting to make it big. Burnet began on drums when he was five and later played piano and banjo. At school at one point he traded a classmate his watch for a trumpet and quickly mastered the instrument. He studied at Yale, played for a time in hotel bands in Bermuda, was with Eddie Neibauer's Orchestra in Chicago, and then joined Barnet's up-and-coming orchestra. Burnet can be heard on such recordings as "Cherokee," "Redskin Rhumba," and "The Right Idea," among many others, and was Barnet's top sideman during the period. After leaving the band, he led a short-lived interracial sextet at Café Society and Nick's. Burnet rejoined Barnet for part of 1941-1942 but was never again a full-time musician after he departed the second time. He served in the Army during World War II, worked in the electronics field after the war, recorded with Freddie Wacker's Windy City Six in 1957 (for the tiny Dolphin label), and moved to Mexico in 1958. In later years, Bob Burnet sometimes played flute with a local symphony orchestra.