Baumann is a 1971 graduate of Hueytown High School and was a biology major at UAB. Prior to being elected mayor, he was the manager of Baumann Coatings in Bessemer. Baumann is a member of Grace Lutheran Church, Hueytown Lions Club, Hueytown High School Quarterback Club and the Hueytown Beautification Board.
In the 2016 general election, Baumann lost the mayor's race in a runoff to Steve Ware. In 2020 general election, Baumann, a Republican, was defeated by Democrat Eric Burks to be the Assistant Tax Collector of the Bessemer Division of Jefferson County.