Baesler was born in Lexington, Kentucky. He graduated from the University of Kentucky in 1963 and earned a law degree in 1966. While at the university, Baesler played basketball under legendary coach Adolph Rupp. Over his final two seasons, Baesler maintained a per game average of 10.3 points, 4 rebounds, 3 assists, while shooting 83% from the foul line.
After graduating from law school, Baesler practiced law and served as an administrator for Legal Aid, Inc., a nonprofit entity that provides free legal services to indigent persons facing criminal charges. He later served as a District Court Judge in Fayette County for some years before serving as mayor of Lexington from 1982 to 1993.
In 1991, Baesler ran for governor in the Democratic primary and was narrowly defeated by Brereton Jones, who won the general election.
In 1992, Baesler was elected to the U.S. House of Representatives for the 6th Congressional district of Kentucky after 14-year Republican incumbent Larry Hopkins retired; Hopkins had never recovered from being heavily defeated by Jones in the 1991 governor's race. He served there for three terms. In 1996, he defeated Ernie Fletcher by a vote of 125,999 to 100,231. He left his seat in 1998 to run for the Senate seat of retiring Democratic whip Wendell Ford. Baesler won a narrow primary victory over Louisville businessman Charlie Owen and Lieutenant Governor Steve Henry, but was very narrowly defeated in the general election by fellow congressman Jim Bunning, a Republican. Baesler assumed early on that he had no chance of carrying Bunning's 4th District, based in the Cincinnati suburbs. He aired almost no ads in the Cincinnati television market. This came back to haunt Baesler in November, as Bunning swamped him in the 4th, winning by a margin that Baesler couldn't make up in the rest of the state. Baesler barely won his own district, which came as something of an embarrassment.
In 2000, Baesler tried to regain his House seat against the Republican who had replaced him, Ernie Fletcher. Fletcher had lost badly to Baesler in 1996 after Baesler painted him as an extremist. However, by 2000 Baesler was badly wounded from his narrow loss to Bunning two years earlier. He wasn't helped when Democratic presidential candidate Al Gore all but conceded Kentucky to Republican George W. Bush in August (Bush went on to win Kentucky by 15 points). Earlier, all four of Lexington's TV stations pulled a Democratic Congressional Campaign Committee ad for Baesler, claiming the ad falsely charged Fletcher with cutting funding for education. In the general election, Fletcher defeated Baesler by 18 points.