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. He resigned after losing the 2008 FIFA Club World Cup to Manchester United.

On January 15, 2009, the IFFHS ranked him third among the top ten club coaches around the world, only behind Sir Alex Ferguson and Dick Advocaat. He was also voted the 2008 South American Coach of the Year by Uruguayan newspaper El País. 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. He lost the 2011 Copa Sudamericana finals to Universidad de Chile.

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. He subsequently signed with São Paulo FC from Brazil on December 17, 2015. President of club, Carlos Augusto de Barros e Silva, said the following words: “I am very happy for signing with a winning coach […]”.

After just one season in Brazil, Bauza was appointed as the new manager of the Argentine national team, on 11 August 2016. He was relieved of his duties on 11 April 2017 with the Albiceleste placed fifth in CONMEBOL World Cup qualifying, with only four teams guaranteed a qualification spot.

He was appointed manager of Rosario Central in May 2018. Bauza guided Rosario Central to win the Copa Argentina 2018. https://www.espn.com.ar/video/clip/_/id/5055053. After a period with bad results, Rosario decided to fire Bauza on 23 February 2019.