Bambuck took part in his first Olympic Games in Tokyo in 1964. At the 1966 European Championships in Budapest, he won the gold medal in the 200 m and in the 4 × 100 m relay, as well as the silver medal in the 100 m.
He competed in the 1968 Summer Olympics held in Mexico City in the 100 metres (finalist) and in the 4 x 100 metre relay where he won the bronze medal with his team mates Gérard Fenouil, Jocelyn Delecour and Claude Piquemal. In the 100 and 200m. individual men's final he finished fifth with times of 10.16 and 20.51 seconds respectively. Earlier in 1968 he had equalled Armin Hary's eight-year-old European record of 10.0 seconds.
He retired from sprint after the Mexico games, aged 23.
In the mid-eighties, he became head of sport for the commune of Épinay-sur-Seine. From 1988 to 1991, he was minister of Youth and Sports under Michel Rocard. He then held senior positions in the civil service.
Bambuck set out to study medicine but dropped out. He then worked a time for the automobile manufacturer Renault, before his athletic career.
He had the honour of starting the 24-hour Le Mans race.