Bill Basie stopped in Tulsa the first time in 1926. He was traveling on the TOBA circuit (Theater Owners Booking Association was the vaudeville circuit for African American performers in the 1920s and 1930s) with the show Gonzelle White and Her Big Jazz Jamboree. In this show Basie played piano, a villain in a skit and played a ballyhoo in the streets to drum up business. The show was in town for a week to 10 days and the group was put up at the Red Wing Hotel (actually a boardinghouse) on Greenwood Avenue.
In his memoir Good Morning Blues, Basie recalls one morning, as he was sleeping in late, he awoke to music he thought must be coming from a Victrola in another room. He threw on his clothes and stumbled downstairs and encountered The Walter Page Blue Devils, a band from Oklahoma City, playing a ballyhoo on the street. The groups verve and dynamics dazzled him and though he met the band and was invited to join, it wasn't until a year later that he did. Basie is quoted as saying that The Blue Devils were "the happiest band I've ever been in. Everybody seemed to be having so much fun just being up there playing together, and they looked good and sounded good to boot." The band broke up in the early 1930s.
Also in his memoir he says he returned to Tulsa in 1935 for a one-night gig at a dance hall, but no other information is available.
By the time he returned to Tulsa, when the following pictures were taken, he was known as Count Basie and had several hits out, including "Swingin' The Blues", Jumpin' At The Woodside" and his theme song, "One O'Clock Jump". This show is sponsored by Columbia Records which he joined in 1939, shortly after his "discovery" at The Famous Door in 1938. It looks like it was in the early 1940's.
And now, for your listening pleasure, I give you Count Basie and his orchestra performing Big Band Basie Boogie in the 1943 movie "Top Man" - the video quality isn't so great but the music is: