In 2008, Bauza made history by becoming the first manager ever to lead an Ecuadorian club to victory in an international tournament, winning that year's Copa Libertadores.

His team included three Argentine players (Damián Manso, Claudio Bieler and Norberto Araujo), along with Paraguayan midfielder Enrique Vera, strong wingers Luis Bolaños and Joffre Guerrón and veteran goalkeeper and penalty shootout hero José Francisco Cevallos.

[2] On 15 January 2009, the IFFHS ranked him third among the top ten club coaches around the world, only behind Sir Alex Ferguson and Dick Advocaat.

After a spell with Saudi Arabian side Al-Nassr FC, Bauza returned to LDU Quito in December 2009, replacing 2009 Copa Sudamericana-winning manager Jorge Fossati.

In 2013, he joined San Lorenzo de Almagro of the Argentine Primera División, where he led the club to its first ever Copa Libertadores title in 2014.