He graduated from the Radnóti Miklós Grammar School of Eötvös Loránd University, and was then admitted to the Corvinus University of Budapest (then Marx Károly Economics University), where he obtained a degree in 1968. In 1984, he defended his Doctor of Philosophy thesis in economics.
His research areas are the Eastern European planned economies. He has a younger sister, Judit (born 1951). Bauer married Aranka Verebélyi, an economist in 1969.
They have two children: János (born 1970) and Zsuzsa (born 1972).
He worked for the Research Institute of Economics of the Hungarian Academy of Sciences (MTA). Later he was promoted to Senior Researcher.
In 1988, he served as a university professor of the Department of Comparison and Transformation of Economic Systems in the University of Frankfurt, and later became head of that department. He also served as a project manager for the National Fund for Scientific Research from 2004 to 2009.
Later he was one of the leading figures of the Democratic Opposition.
He published under the pseudonym of Dénes Csonka for the illegal liberal newspaper Beszélő. He resigned from that position in 1988 and was one of the initiators of the New March Front (Új Márciusi Front). In 1985, the Communist party prevented his participation at the parliamentary elections.
He was a candidate for the next parliamentary elections but did not obtain a mandate.
During the 2002 parliamentary election he lost his mandate. He left the party in 2007 because he disagreed with the policy of the party leadership and what he considered its flawed economic policies.
He joined the newly formed Democratic Coalition (Denmark) led by former prime minister Ferenc Gyurcsány and became its one of the deputy chairmen on November 6, 2011. He resigned from his position due to personal and ideological reasons on 26 May, 2014.
Bauer joined Hungarian Socialist Workers" Party (MSZMP) in 1966 but was expelled from the party eight years later, in 1974 because he did not support further tightening of the approval of abortion. In 1985 he was elected to a member of the National Council of the Patriotic People"s Front.
He became a member of the Hungarian Economics Society in that same year. He was a member of the Commission of Economics of MTA between 1991 and 1994. In that same year he became one of the founding members of the Alliance of Free Democrats (Szabad Demokraták Szövetsége (Alliance of Free Democrats)).
He was appointed member of the new party"s leadership.
He became a member of the National Assembly in 1994 and 1998 from the Szabad Demokraták Szövetsége (Alliance of Free Democrats)"s national list.