Foster was born in Gloucestershire and began racing motorcycles in 1932. He rode a New Imperial at the Manx Grand Prix in 1933 and 1934, finishing second in the 1934 Lightweight race. His first Isle of Man TT appearance came in 1935 on a New Imperial in the Lightweight TT, where he did not finish.
Foster took his first TT victory in the 1936 Lightweight TT aboard a New Imperial, swapping the lead several times with Stanley Woods on a DKW before Woods retired on the final lap, leaving Foster to win at a then-record average speed of 76.28 mph. This result was historically significant: it was the last time a British-made motorcycle won a Lightweight TT. After New Imperial withdrew factory support following the 1936 event, Foster switched to an AJS 350 cc R7, riding it from 1937 to 1939.
When racing resumed after the Second World War, Foster won the first post-war Junior TT in 1947, averaging 80.31 mph on a Velocette and finishing four minutes clear of the second-place finisher. He was runner-up to Freddie Frith in the 1948 Junior TT. In the 1949 Senior TT he set a post-war lap record of 25 minutes 14 seconds (89.75 mph) on a Moto Guzzi and held a 57-second lead before retiring with mechanical trouble.
The 1950 season brought Foster's finest achievement. The principal opposition came from the Norton factory team, which opened the season by sweeping the top three positions at the Isle of Man TT with Artie Bell and Geoff Duke among their riders. Foster responded by winning the Belgian Grand Prix ahead of Bell and Duke, then followed with victories at the Dutch TT and the Ulster Grand Prix, supplemented by a second place at the Swiss Grand Prix. This campaign earned him the 1950 FIM 350 cc World Championship, defeating the powerful Norton works effort with a largely private effort.
Foster also competed in the 1949 World Championships, where he finished second to Freddie Frith at both the Dutch TT and the Belgian Grand Prix on a Velocette. He retired from racing after the 1951 Isle of Man TT and settled in Dorset, where he operated garages in Blandford and Parkstone until his death in 1982.
Bob Foster's career bridged the pre-war British club racing scene and the inaugural seasons of the FIM World Championship. His 1950 title — secured against Norton's factory resources — remains one of the notable achievements of early Grand Prix motorcycle racing, demonstrating how a determined private rider could prevail over the most organised factory campaigns of the era.