Burness was born in Los Angeles. His animation career began in 1931, working for Romer Grey and Ted Eshbaugh on Goofy Goat Antics and the unreleased Binko the Cub. In 1933 he transferred to Van Beuren Studios, where he animated the film adaption of The Little King. Burness transferred to Harman-Ising in 1936 and to Metro-Goldwyn-Mayer in 1938. He animated Tom and Jerry at MGM until 1945. Burness worked briefly for Warner Brothers in 1948 and 1949, animating a number of Looney Tunes and Merrie Melodies shorts. He left Warner to become a director for United Productions of America, animating the popular Mr. Magoo series. Two of his Mr. Magoo shorts, When Magoo Flew (1954) and Mr. Magoo's Puddle Jumper (1956), won Academy Awards for Best Short Subject. In 1958 Burness left UPA to join Jay Ward Productions as director of Rocky and his Friends and Hoppity Hooper. While working for Jay Ward he co-wrote and was hired to direct 1001 Arabian Nights, featuring Mr. Magoo. Following disputes with producer Stephen Bosustow, he left the project and was replaced by Jack Kinney. Burness died of cancer in 1969.