Bunster is an Irish surname. People with this name include:
Arthur Bunster (1827 - 1891), historical Member of Parliament from British Columbia, Canada
Claudio Bunster (Teitelboim) Weitzman (born 1947), Chilean scientist
Enrique Bunster (1912-1976), Chilean novelist and playwright
Jorge Bunster (born 1953), Chilean businessman and politician
Rolando Gonzalez-Bunster (born c. 1949), US-based Argentine businessman