In the interim, from 1941 to 1945, he was a United States Naval Reserve Lieutenant.

He was engaged in the private practice from 1947 to 1953, then became head of the Criminal Division of the United States Attorney's Office for the Southern District of New York until he resigned in 1955 to enter private practice.

[1] Bauman was nominated by President Richard Nixon on December 2, 1971, to the United States District Court for the Southern District of New York, to a new seat created by 84 Stat.

[1] In resigning, he cited the insufficient pay, then $40,000 per year, allotted to federal district judges.

[2][3] Following his resignation, he returned to private practice, serving until his death on November 20, 1989, in New York City.