Bush was born in 1956 and studied Fine Art at Central School and Goldsmiths College, London. He taught himself how to make films while a member of the London Film-makers Co-op and Chapter Film Workshop in Cardiff. From 1981 to 1993 he taught film-making, establishing a film workshop in South London and supervising a wide variety of courses and the production of numerous student films. between 1995 and 2001 he taught on the visual arts course at Goldsmiths. He has lectured, run workshops and tutored at numerous art and film courses around the world including the Media Academy of Cologne, National Film Board of Canada, The Netherlands Institute of Animation Films, CalArts, Centro Sperimentale di Cinematografia, Turin, St Lukas in Brussels, KASK in Ghent, Anadolou University in Turkey, Lucerne University of Applied Science and Arts, and the Royal College of Arts, Duncan of Jordanstone and the National Film and Television School in Britain.