Born in Bologna, Bucci spent a few years in the third and second levels (winning the 1992–93 Serie B title with Reggiana). He made his Serie A debut playing for Parma, in a league match against Udinese on 29 August 1993. He soon achieved prominence during a particularly successful stint with the club, winning an UEFA Supercup in 1993, and an UEFA Cup in 1995; he also received runners-up medals in the Coppa Italia, in the Cup Winners' Cup, in the Supercoppa Italiana, and in Serie A with the club. Bucci was the starting keeper for Parma when they won the UEFA cup in 1995. At Parma, however, Bucci was soon overtaken by the emergence of 18-year-old "Primavera" keeper Gianluigi Buffon during the 1996–97 season. Bucci started the season as the starting keeper for the first seven games. After dispute with the first time coach Carlos and emergence of Buffon, moved Bucci to leave the team in order to play more regularly.