An Inter youth product, Bet was later promoted to the senior squad, before manager Helenio Herrera brought him to Roma, where he made his breakthrough, winning a Coppa Italia, and also earning a call-up to play for the Italy national football team. After five seasons with Roma, and one with Verona, he joined A.C. Milan in the summer of 1974. He was usually paired alongside a sweeper in the team's defence: first Maurizio Turone, and later a young Franco Baresi; he won a second Coppa Italia with Milan, and was a member of the team that won club's tenth league title in 1979.