Bailey began as an apprentice at Austin's Longbridge plant in 1942, at a time when the factory was producing Short Stirling bombers for the Royal Air Force. He built experience at Daimler and Rover in Coventry before returning to Austin after it merged into the British Motor Corporation in 1952. In 1956 he moved to the United States and joined American Motors, where he worked on AMC's first in-house V8 engine following the collapse of a deal to purchase Packard units.
In 1958 he transferred to Ford's headquarters in Dearborn, Michigan, joining the engine department before being moved into the Experimental Department by Roy Lunn. There he worked on Ford turbine car prototypes and was part of the team that built the two-seat Ford Mustang I concept in 1962.
When Ford committed to a serious Le Mans campaign in 1963, Bailey was moved back to England as chief draftsman for Ford Advanced Vehicles Ltd in Slough. The basis of the programme was Lola's Ford-powered mid-engined sports car of 1963, with Eric Broadley taking initial responsibility for overall design. Bailey subsequently assumed responsibility for reengineering the chassis from aluminium to steel to achieve the durability required for a 24-hour race, and to handle the added weight of the more powerful Ford Fairlane engine.
By 1966 he was based at Alan Mann Racing in Byfleet, Surrey, while remaining employed by Ford of Europe. That year, eight GT40 Mark IIs were prepared for the 24 Hours of Le Mans; all factory Ferraris had retired by the 17-hour mark, and three Fords survived to score an historic 1-2-3 finish. For 1967, while Ford USA concentrated on the GT40 Mk IV for their main assault, Bailey redesigned the two GT40s entered by John Wyer's JW Automotive for the manufacturers' championship. These lightweight variants — fitted with a slimmer windscreen, altered roofline, cut-off tail, and aluminium body panels — were entered as the Mirage M1 with Gulf Oil sponsorship.
At the end of 1966 he completed the design of the Honker II, a Can-Am car built by Alan Mann Racing and run by Holman Moody, powered by an injected Ford V8. The FIA's 1968 regulation changes — capping engine capacity at 3 litres for the Group 6 prototype class — prompted Ford Europe to task Bailey with creating a new car, resulting in the Ford P68, which was revised to the P69 for 1969; both were built and run by Alan Mann Racing. During his Alan Mann years, Bailey also designed the bodies of two aluminium gull-wing cars used in the 1969 Gerry Anderson science-fiction film Doppelgänger, and contributed suspension and brake work — including development of rear disc brakes — to the Ford Escort's rally and racing programme.
After Alan Mann Racing wound down at the end of 1969, Bailey established himself as a freelance designer and set up his own design office at Gomm Metal Developments in Woking in 1970. His first single-seater was the Alfa Romeo-powered Mildren Mono for Australian patron Alec Mildren; Frank Gardner drove it to sixth in the 1969 Tasman Series and Kevin Bartlett won the 1969 Australian Drivers' Championship in the same car.
Gardner then commissioned a monocoque Formula 5000 car for the 1970 UK season, but signed with Lola instead; the design passed to Palliser Racing Cars as the Palliser WDA1. During the summer and autumn of 1970 Bailey worked on a secret Ford rally project that became the notable but unused Ford GT70. He went on to design the Cosworth DFV-powered Gulf Mirage M6 sports car for JW Automotive's 1972 and 1973 World Sportscar Championship campaigns. In 1971 Frank Williams commissioned him to design the Politoys Ford FX3 of 1972 and the Iso Rivolta Ford FX3B of 1973, though neither car achieved significant results.
His consultancy work continued through the 1970s and 1980s and included the Ford Fiesta Group 5 Rally Car (1978), the Ford C100 Group C car (1982), and the EMKA Racing Aston Martin Group C cars of 1983 and 1984. He also contributed chassis work to the AC Ace in 1994, one of his final known projects before his death in June 1997.