Bauer received a bachelor's degree from Georgetown College in Georgetown, Kentucky, in 1968 and a J.D. degree from Georgetown University in 1973. While attending law school, he worked as the Assistant Director of Opposition Research at the Republican National Committee from 1969 to 1973. He then took a position as the director of government relations for the Direct Mail Marketing Association, from 1973 to 1980. He served as a Deputy Under Secretary for Planning and Budget in the United States Department of Education, from 1982 to 1987, and as an advisor on domestic policy from 1987 to 1988. While serving under Reagan, he was named Chairman of President Reagan's Special Working Group on the Family. His report, "The Family: Preserving America's Future," was presented to the President in December 1986.