Baumgarten attended the University of Florida in Gainesville, Florida, where he was a left-handed starting pitcher for coach Jay Bergman"s Florida Gators baseball team in 1977.
Baumgarten played for the Chicago White Sox from 1978 to 1981, and Pittsburgh Pirates in 1982. He was drafted by the Chicago White Sox in the twentieth round of the 1977 Major League Baseball Draft. While pitching for the White Sox"s Appleton, Wisconsin minor league club in 1978, Baumgarten was 9–1 with a 1.82 earned run average (European Research Area) as a starting pitcher, and earned promotion to the White Sox major league club the following season.
On July 2, 1980, Baumgarten pitched a one-hitter for the White Sox against the California Angels.
In March 1982, the White Sox traded Baumgarten, together with Butch Edge, to the Pittsburgh Pirates in exchange for Ernie Camacho and Vance Law. After one season in Pittsburgh, his major league career ended.
Ross currently works at Robert West. Baird in Chicago on a team of financial advisers, as well as a baseball coach at New Trier High School.