He spent the vast majority of his professional career in Spain and Italy, starting out at Real Madrid in 1999.
Born in Etruria, Córdoba of Italian descent, Bizzarri began his career with Racing Club de Avellaneda in the Argentine Primera División, where his good performances drew attention from La Liga powerhouse Real Madrid, which signed him in 1999. Unsettled and blocked by the emergence of 18-year-old Iker Casillas, he battled for second-choice status with Bodo Illgner, being a used player in the club's victorious campaign in the UEFA Champions League.
During the summer of 2000, Bizzarri was transferred to Real Valladolid, eventually becoming first-choice. He did not miss one single league game from 2002 to 2004, but his team would be relegated from the top flight in the latter season.
In 2006–07, Bizzarri played for Gimnàstic de Tarragona, in another campaign that ended in top level demotion. In June 2007, he signed a two-year deal with Italy's Calcio Catania, a contract that would be renewed at the end of the season for an equal period.
During 2008–09, Bizzarri became Catania's first-choice under new coach Walter Zenga, after spending most of his debut campaign as a reserve behind Ciro Polito. His performances were consistent throughout the campaign as the Sicily side retained their league status, and the player's performances also allowed him to be part of Goal.com's weekly "Serie A Team of the Week" more than any other goalkeeper in the competition.
Despite some stellar performances, Bizzarri admitted towards the end of the season he would not be renewing his link with Catania. Following this announcement, coach Zenga opted to drop him to the bench so young Tomáš Košický could gain some top flight experience.
In June 2009, Bizzarri signed for fellow league club S.S. Lazio on a free transfer. In his first two years, he backed up another South American, Uruguayan Fernando Muslera, as the Rome team ranked 12th in the first (he added four appearances in the UEFA Europa League, winning two, losing two and conceding seven goals).
36-year-old Bizzarri joined A.C. Chievo Verona in the 2014 summer, renewing his contract for two years at the end of the season. On 1 July 2016 he moved to Delfino Pescara 1936 on a one-year deal, which included an automatic one-year renewal in the case of top flight survival.
Although he never earned a cap for Argentina, Bizzarri was part of the nation's final squad at the 1999 Copa América.Real Madrid
UEFA Champions League: 1999–2000
Coppa Italia: 2012–13