Bourne lived in Pukekohe, Auckland, near his workshop, with his wife Peggy and their three children. His nickname "Possum" originated in his youth, when he crashed his mother's Humber 80 while swerving to avoid a possum on the road at night. The story became part of the legend surrounding a driver whose name would eventually be synonymous with Australasian rallying.
Bourne became closely identified with Subaru cars throughout his career, beginning with the turbocharged Subaru Leone RX, progressing to the Legacy (sold in Australia as the Liberty), and ultimately becoming most associated with the Impreza WRX. In 1993 he became the first New Zealand resident to hold a works contract in a FISA rally championship, driving a Subaru Legacy for Prodrive.
He drove for the Subaru World Rally Team in events including Rally New Zealand, Rally Australia, and rallies in Indonesia, where he was partnered with Richard Burns during the mid-1990s. He later continued to win multiple Australian Rally Championship titles with Subaru Rally Team Australia. Subaru Japan presented him with a black limited-edition Subaru Impreza WRX STi for personal use, a mark of the esteem in which the manufacturer held him.
A significant blow came in 1993 when Bourne's best friend and co-driver Rodger Freeth died in an accident during Rally Australia. The tragedy almost ended Bourne's career. Encouraged by the Freeth family, he returned to competition. From that point he carried a "ROJ" license plate on the front of his rally cars in memory of Freeth.
At the time of his death, Bourne had returned to international competition by entering the Production World Rally Championship class in a production-spec Subaru Impreza.
On 18 April 2003, Bourne suffered serious head injuries in a non-competitive car crash on Waiorau Snow Farm Road near Cardrona, not far from Wānaka in the South Island of New Zealand. He had been driving his Subaru Forester over the road that was to serve as the course for the Race to the Sky hillclimb event. His vehicle collided head-on with a Jeep Cherokee driven by rally driver Mike Barltrop. Bourne was transported to Dunedin Hospital, where he died on 30 April 2003 after life support was withdrawn.
Barltrop was subsequently arrested on a dangerous driving charge. After pleading guilty to aggravated careless use causing death, he was sentenced to 300 hours of community work, an 18-month driving disqualification, and a reparations order of $10,000 divided between Dunedin Public Hospital's intensive care unit and the Possum Bourne Education Trust.
Bourne's autobiography, Bourne to Rally, was completed just days before his death. A bronze memorial statue was unveiled at the site of his fatal accident one year later, and was subsequently relocated to Pukekohe town square in April 2013 in conjunction with the ITM 400 V8 Championship parade. In 2005, his widow Peggy Bourne entered Race to the Sky as a tribute to him, despite having no formal rally driving experience. His eldest son Taylor competed in the 2013 Possum Bourne Memorial Rally.
Bourne remains a towering figure in New Zealand and Australian motorsport, remembered as the driver who made Subaru and rally racing synonymous in the Australasian region.