Bunbury was born in Glastonbury, England in 1940, to an Australian father and an English mother. He graduated with an honours degree from the University of Durham in 1963, then decided to visit his father's homeland, Australia. He worked on his cousin's farm and bed and breakfast in Broomehill for a few months before moving to Perth, where he taught English at Guildford Grammar School. A visit to the school by an ABC television crew introduced Bunbury to ABC worker Roger Penny. Assisted by Penny's connections, Bunbury gave up teaching to join the education unit of the ABC in May 1969.
Bunbury's first couple of years at the ABC consisted of radio work. He moved to television shortly afterwards to present a children's program called Here in the West. While filming this show, he was inspired to record a 30 minute documentary about settlers in Denmark. The documentary's unexpected popularity prompted Bunbury to continue this work, and he travelled around Western Australia recording programs on the state's history.
In 1985, historian and broadcaster Tim Bowden founded a social history unit, with Bunbury's support in lobbying the ABC. Bunbury had seen from his previous work there was a large potential audience for history topics, and he signed on as the host of Talking History. He then worked on the programmes Hindsight, Verbatim, Street Stories and Encounter. He retired from the ABC in 2007. Bunbury said, "I wanted to go while I was still doing good work. I think I've quit while I was, hopefully, still winning races. I think maybe some [journalists] retire too early. Perhaps some go on [working] too long. You try to pick the right time."
Bunbury's documentary series covered such topics as Cyclone Tracy, Australia's involvement in the Vietnam War, and the granting of equal wages to Aboriginal stockmen in 1966. His work had a strong focus on Indigenous Australian history. Bunbury won awards for his radio programmes and series, including a gold medal from the New York Radio Festival for "Timber for Gold", a look at gold mining in Kalgoorlie, and a UN Australia Peace Prize for "The War Rages On", about Australians in Vietnam.
His interest in oral history and recording of people's memories has created a vast resource in the Western Australian state library, Battye Library, of recorded interviews with people from various documentaries and programmes. Journalist Andre Malan has described this as Bunbury's legacy, "a priceless archive of the State's rich oral history that would otherwise have been lost forever".
Bunbury has published extensively with the Fremantle Press, and is currently Adjunct Professor of History and Media at [[Murdoch University] where he was also awarded an Honorary Doctorate in Literature in 2008 for services to broadcasting and history].
Bunbury and his wife,Jenny now live in Margaret River]]. They have two daughters, Alison and Kate and two grandsons, Sam and Jack.
- Bunbury, Bill. (2010). Till the stream runs dry. A history of hydrography in Western Australia. Department of Water WA ISBN 978-1-921789-38-0
- Bunbury, Bill. (2006). Caught in time: talking Australian history. Fremantle, WA: Fremantle Arts Centre Press. ISBN 1-921064-84-6
- Bunbury, Bill. (2002). It's not the money it's the land: Aboriginal stockmen and the equal wages case / talking history with Bill Bunbury. North Fremantle, WA: Fremantle Arts Centre Press. ISBN 1-86368-366-6
- Bunbury, Bill. (2002). Timber for gold: life on the Goldfields woodlines / talking history with Bill Bunbury. North Fremantle, WA : Fremantle Arts Centre Press. ISBN 1-86368-372-0
- Bunbury, Bill. (1998). Unfinished business: reconciliation, the republic and the constitution Sydney: ABC Books. ISBN 0-7333-0650-0
- Bunbury, Bill. (1995). Rabbits & spaghetti: captives and comrades, Australians, Italians and the war, 1939-1945 / talking history with Bill Bunbury. Fremantle, WA: Fremantle Arts Centre Press. ISBN 1-86368-122-1
- Bunbury, Bill. (1994). Cyclone Tracy: picking up the pieces / talking history with Bill Bunbury. South Fremantle, WA: Fremantle Arts Centre Press. ISBN 1-86368-112-4
- Bunbury, Bill. (1993). Rag, sticks & wire: Australians taking to the air Sydney: ABC Books. ISBN 0-7333-0273-4
- Bunbury, Bill. (1993). Reading labels on jam tins: living through difficult times South Fremantle, WA: Fremantle Arts Centre Press. ISBN 1-86368-031-4
- Bowden, Ros, & Bunbury, Bill. (1990) Being Aboriginal : comments, observations and stories from Aboriginal Australians / from the ABC Radio programs by Ros Bowden and Bill Bunbury. Sydney: ABC Enterprises. ISBN 0-7333-0023-5
- Simper, Errol (2007-03-22). "RN's quiet achiever brought the past to life". The Australian. p. 18.
- "How the Quest Was Won: Bill Bunbury". Australian Broadcasting Corporation. 2005-11-18. Retrieved 2008-09-04.
- Malan, Andre (2003-05-17). "Bunbury's history". The West Australian.
- "Radio National: Hindsight Presenters". Australian Broadcasting Corporation. Retrieved 2008-09-04.
- "Fremantle Press: Authors: Bill Bunbury". Fremantle Press. Retrieved 2008-09-04.