Bär received his musical training in his home city of Dresden, studying at the city's Hochschule für Musik. His career has concentrated on lieder and on the lyric baritone roles of the operatic repertoire. Many of his early lieder performances were accompanied by the late Geoffrey Parsons.
His operatic debut was in 1981 in Dresden and he was a member of that city's opera company (Semperoper) from 1985 to 1991. His voice has been compared favorably with that of Dietrich Fischer-Dieskau.