Early in the 1940s he left this group to play alto saxophone in the big band of Jack Teagarden.
Jack Kerouac | Jack Nicholson | Jack Nicklaus | Jack the Ripper | Jack London | Jack Kemp | Jack Kirby | Jack Lemmon | Jack Black | Jack Abramoff | Jack Dempsey | Jack Benny | Jack White | Wolfman Jack | Union Jack | Jack White (musician) | Jack and the Beanstalk | Jack Johnson | Jack Charlton | Jack Palance | Jack Daniel's | Jack | Jack Paar | Jack Layton | Jack Straw | Jack Vance | Jack Bruce | Jack Warden | Jack's Mannequin | Jack in the Box |
Jack Teagarden, Tommy Dorsey and his Clambake Seven, Coleman Hawkins, and Doc Evans in 1947 also recorded the song under the title "Original Dixieland One-Step".
His ensemble featured a large number of sidemen who went on to become noted for their own achievements, including Gene Krupa, Jack Teagarden, Frankie Carle, Jack Jenney, Toots Mondello, Irene Daye, Clark Yocum, Floyd O'Brien, Spud Murphy, Boots Mussulli, Brad Gowans, Turk Murphy, Teddy Grace, and Don Fagerquist.
After the break-up of the Crosby band, Bauduc organized his own small groups (often in a swing or even bebop style), rejoined Bob Crosby for occasional reunions, worked with Jimmy Dorsey (1948) and Jack Teagarden (1952–55), before joining fellow ex-Bobcat Nappy Lamare in a highly successful dixieland band that lasted until 1960, after which Bauduc went into semi-retirement in Bellaire, Texas.
In the 1950s he played with Bill Baker and Jack Teagarden; his tenure with Teagarden lasted from 1958 to 1963 and includes many of Teagarden's recordings on Capitol Records and all his releases on Roulette Records.
He had many gigs in New York in the 1930s and 1940s, including time with Joe Haymes (1934-35) and Tommy Dorsey (1935), Ray Noble (1936), Benny Goodman (1936), Lana Webster, Glenn Miller (1937), Bob Crosby (1937-39), Bobby Hackett (1939), Bob Zurke, Jack Teagarden, Bud Freeman (1942), George Brunies, Bobby Sherwood (1943), Miff Mole, Art Hodes, Horace Heidt (1944), and Tiny Hill (1946).