Bauza started his career with Argentine Primera División side Colón. His first appearance for the club came on 22 October 2016 in loss at home to Patronato.[1][2][3] He made three further appearances in the 2016–17 season, prior to being loaned out for the following campaign to Juventud Unida.[1][4] He scored the first two goals of his senior career in April 2018 against Deportivo Riestra and Santamarina respectively.[1] Bauza signed for fellow club Gimnasia y Esgrima on loan on 12 July 2018.[1] One goal in twenty-two games followed, as they reached the promotion play-offs.[1]
On 29 July 2019, Bauza headed to Poland to join Polish first division outfit Górnik Zabrze on a season-long loan; having trained since June.[5][6] He made his bow in a league defeat away to Wisła Kraków on 5 August.[1] Bauza played in the fourth tier on 11 August for their reserve team Górnik II Zabrze, notably scoring against Ruch Zdzieszowice in III liga.[7][8] On 17 February 2020, the Polish club confirmed that the loan deal had been terminated and that Bauza had joined Romanian club FK Csíkszereda.[9] He had impressed the Romanian side whilst playing against them for the Polish outfit in a friendly match on 25 January.[7][10]
Bauza scored five goals in eight friendlies upon joining Miercurea Ciuc, prior to making his competitive debut in Liga II during a 6–0 home loss to UTA Arad on 24 February.[1][10] He initially signed for just six months, though soon extended his stay there for another twelve months.[10]
In August 2022, FC U Craiova's president Adrian Mititelu rejected a €2 million bid from FCSB.[11] On 14 September 2022, Bauza signed a contract extension, with his release clause set at €8 million.[12]
Personal life
Bauza's father, Marcelo, was also a footballer.[13]