Bell grew up near Pagham Harbour, West Sussex, and was encouraged by his stepfather Bernard Hender to take up racing with a Lotus Seven in 1964. He won his first race at Goodwood that March and progressed rapidly, graduating to Formula Three in 1965 in a Lotus 31, then switching to a Lotus 41 in 1966 and scoring his first victory again at Goodwood. By 1967 he had accumulated seven wins.
Bell entered Formula Two with a privateer Brabham BT23C operated by his stepfather's Church Farm Racing team, and his performances caught the attention of Enzo Ferrari. He made his Formula One Grand Prix debut for Ferrari at the 1968 Italian Grand Prix at Monza. He raced the experimental four-wheel-drive McLaren M9A in its only ever race at the 1969 British Grand Prix at Silverstone. Further outings followed for the Surtees team, his best World Championship result being sixth place at the 1970 United States Grand Prix in a Surtees TS7. He also drove for the Tecno and Wheatcroft teams, and finished second in the 1970 European Formula Two Championship in a Brabham BT30 for Wheatcroft Racing.
Alongside his Formula One and sportscar activities, Bell contested the British Saloon Car Championship during several seasons. He won the 1973 Silverstone RAC Tourist Trophy driving a BMW 3.0CSL with Harald Ertl, a victory that reflected his adaptability across different car types. His saloon car outings were consistent with a career pattern of accepting the widest possible variety of machinery rather than confining himself to a single discipline.
Bell's enduring legacy rests on his record in long-distance sportscar racing. His association with Le Mans began in 1970 in a works-entered Ferrari 512 with co-driver Ronnie Peterson, and he would make his last Le Mans start in 1996 in a McLaren F1 GTR — a span of 26 years.
He won Le Mans five times: in 1975 sharing a Gulf Mirage GR8 with Jacky Ickx; in 1981 and 1982 in Porsche 936 and Porsche 956 machinery again alongside Ickx; and in 1986 and 1987 in a Rothmans Porsche 962 shared with Hans-Joachim Stuck and Al Holbert. The 1986 and 1987 victories came during a period of Porsche dominance in Group C racing and also contributed to Bell winning the World Sportscar Championship twice, in 1985 and 1986.
At the 24 Hours of Daytona, Bell won in 1986, 1987, and 1989. He also won the Spa 1000km in 1974 (sharing a Mirage M6 with Mike Hailwood), 1975 (an Alfa Romeo Tipo 33TT12 with Henri Pescarolo), and 1984 (a Porsche 956 with Stefan Bellof). In 1984, Bell and Bellof also won the Nürburgring 1000km in the same Porsche 956. Bell claimed his highest ever speed at Le Mans at the 1971 test day, reaching a calculated 246 mph on the Mulsanne Straight in the JW Gulf Porsche 917LH.
His eldest son Justin Bell is also a racing driver, and the two competed together at the 1991 Daytona 24 Hours and the 1992 24 Hours of Le Mans. Bell's proudest moment beyond his five Le Mans victories was co-driving with Justin to third place in the 1995 Le Mans in a Harrods-sponsored McLaren F1 GTR on Father's Day.
Bell took part in the filming of the 1970 Steve McQueen film Le Mans and the two became close friends during the shoot. He was hired as chairman for the Spectre R42 supercar project between 1996 and its end in 1997, and in 2001 consulted on the Bentley Speed 8 programme that led to Bentley's Le Mans victory two years later. He serves as a global ambassador for Bentley and is an operating partner of Bentley Naples in Florida.
Bell was awarded the MBE in 1986 for services to motorsport and received four BRDC Gold Stars (1984, 1985, 1986, 1987). He was inducted into the Motorsports Hall of Fame of America in 2012 and the Le Mans 24 Hours Drivers Hall of Fame in 2013, and into the Motor Sport Hall of Fame UK in 2016. He was named an Honorary Life member of the AA in recognition of 50 years in motorsport, and was made a citizen of honour of Angoulême in 2017.