Bagozza started in the European Cup for the first time in Hochfügen in November 2010 and finished 102nd in the parallel giant slalom. He made his debut in the World Cup in December 2014 in Carezza , which he finished in 48th place in the parallel giant slalom. The following month he reached his first podium in the European Cup with second place in the parallel giant slalom in Livigno . At the 2015 Snowboard Junior World Championships in Yabuli , he achieved 33rd place in the parallel giant slalom and eighth place in the parallel slalom. In the 2017/18 season he won three European Cups. In addition, he came third twice and won the parallel classification and the parallel giant slalom classification in the European Cup. In the parallel slalom classification, he finished second. In the following season he came on the podium for the first time in the World Cup with second place in the parallel giant slalom in Rogla and won his first World Cup victory in the parallel slalom in the Secret Garden Ski Resort . At the highlight of the season, the 2019 Snowboard World Championships in Park City , he finished 19th in the parallel giant slalom and 12th in the parallel slalom. He finished the season on 14th place in the Parallel Giant Slalom World Cup, 13th place in the Parallel World Cup and seventh place in the Parallel Slalom World Cup.
In the 2019/20 season, Bagozza achieved five top ten placements, including first place in the parallel slalom in Bad Gastein , ninth place in the parallel world cup and fourth place in the parallel slalom world cup.