Baur made hundreds of recordings for about a dozen different recording companies, including the three major labels, Victor, Columbia and Brunswick. His first recording, If the Rest of the World Don't Want You, was for Victor in 1923. Baur recorded for Victor as a featured soloist, as a member of the Shannon Quartet (known as The Revelers after 1925), as one the vocalists for Nat Shilkret and the Victor Orchestra, and, on occasion, as the vocalist for Paul Whiteman's orchestra, with many of his recordings being listed by Joel Whitburn as "charted." The Encyclopedic Discography of Victor Recordings (EDVR) lists detailed information for Baur's Victor recordings.
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Baur first recorded for Columbia in 1924, with many more Columbia recordings to follow, and for other labels, including Brunswick, Banner, Domino, Emerson, Gennett, Grey Gull, Puritan, Oriole, and Regal, often using pseudonyms.