He was appointed to his first political office in 1973 in La Rioja Province as the secretary of development, under Governor Carlos Menem.

Menem and Bauzá were deposed during the 1976 Argentine coup d'état, and he was detained by the National Reorganization Process a few months later.

He resumed his political career in 1982 and helped establish the "Federalismo y liberación" (Spanish: "Federalism and liberation") faction within the Justicialist Party (PJ), led by Menem.

The state had bought 500,000 school smocks at a much higher price than usual and only delivered a tenth part, despite the payments in advance.

The 1994 amendment of the Constitution of Argentina created the office of the Chief of the Cabinet of Ministers; Bauzá was the inaugural holder in 1995.

[2] His family, which includes five sons and seven grandsons, refused to hold a public funeral, and arranged only a private ceremony.