Born in Italian North Africa, Bandini was three when World War II broke out and the family moved back to Florence where he grew up. He was apprenticed to a local garage in 1951 and after five years had made enough money to open his own garage. He had always wanted to race but until he had his own business did not have the money to do it. He started competing in 1957 in a Fiat 1100 which was borrowed from one of his customers and started out in hillclimb events and the following year he came to the attention of the racing world with a class victory on the Mille Miglia in a Lancia Appia Zagato. Later that year he had enough money to buy a Volpini Formula Junior car and for the next two years he raced in Formula Junior. In the Spring of 1961 Mimmo Dei, the boss of the Scuderia Centro-Sud team, invited Bandini to race an F1 Cooper-Maserati at the non-championship Pau GP. He finished third behind Jim Clark and Jo Bonnier.

   Scuderia Centro-Sud was closed down that winter but he had done enough to impress Enzo Ferrari and he was signed to be one of the drivers at Maranello for the 1962 season. He did mainly sportscar events but raced for the team at Monaco (where he finished third) and won the non-championship Enna GP in Sicily. It was a similar story in 1963. Bandini won the Le Mans 24 Hours with Lodovico Scarfiotti and then Mimmo Dei revived Scuderia Centro-Sud and bought a BRM and Bandini began racing that at the French GP. At the end of the year Ferrari claimed him back and he was number two to John Surtees until 1966 when he replaced the Englishman as Ferrari team leader.

   Bandini's greatest day came in 1964 when he won the first Austrian GP on the bumpy Zeltweg aerodrome circuit although there were other important victories for Ferrari in sporstcars, notably the Targa Florio in 1965 and the Daytona 24 Hours in 1967.

   In May that year he was running second to Denny Hulme in the Monaco GP when he lost control at the chicane and crashed. The car overturned and caught fire and Bandini was trapped beneath the flaming wreck. It was several minutes before he was rescued and his burns were terrible. For three days he fought for his life before succumbing to his injuries.