Born in Chicago, Illinois, Bauer served in the United States Army from 1945 to 1947.

[1] Bauer was nominated by President Gerald Ford on December 11, 1974, to a seat on the United States Court of Appeals for the Seventh Circuit vacated by Judge Otto Kerner Jr.

[1] On April 19, 2018, Bauer wrote the majority opinion striking down Indiana's ban on abortion due to disability as unconstitutional.

Bauer was joined by Joel Flaum, over the dissent of Daniel Anthony Manion.

[2] In 2013, Bauer married Patricia Spratt, an appellate litigator and a shareholder of the firm Shefsky & Froelich.