After beginning his career with Cerromar in the youth categories, Bava made his senior debut with
Progreso in 1998. He joined
Peñarol in 2000, but played rarely before moving to
Juventud de Las Piedras in the following year. Bava signed for
Nacional in 2002, but featured rarely before joining
Bella Vista shortly after. in 2012 In January 2010,
Rosario Central signed Bava on a two-year contract. On 10 January 2012, he returned to Nacional for a third spell. In July 2015, after losing his starting spot, Bava agreed to a deal with
Liverpool Montevideo. After one season as a starter, he signed for
Atletico Bucaramanga in Colombia on 8 July 2016. On 7 January 2017, Bava signed with
Major League Soccer club
Chicago Fire to a one-year contract with two one-year options. His contract was terminated by mutual consent on 18 January 2018, and returned to Liverpool shortly after. In May 2019, Bava confirmed his departure from Liverpool, and returned to Paraguay to join
Guaraní. He left the latter on 6 October 2020 due to personal reasons, and returned to Liverpool the following 5 January. ==Managerial career==