I think Bix honestly believed he was a musical degenerate. He knew how lacking in formal training he was, how he was always getting by with his ear and could only read well enough to get by. He DID feel intimidated by the crack, schooled musicians who could read fly specks and execute any difficult score with aplomb. This lack of training got him fired from the Goldkette band in '24, and he never forgot. He knew he was getting away with murder, and naturally, was not proud of it. He wasn't being modest - only sincere.
The proof of this is that in his quest for musical "legitimacy," he embraced the ideals and tenets of the "symphonic jazz" school, which made extreme technical demands on its practitioners. No mere "Jazz Band" in the '20s could have delivered a reading of "Whiteman Stomp" or "A Rhythmic Dream" or "Humpty Dumpty" without the utmost classical training and discipline. Of course, Bix's natural aptitude and genius got him over many hurdles that would have stymied many another "ear" player. But still he would have paled if he was handed Charlie Margulies' trumpet parts by mistake!
Therefore, I think Bix was completely sincere when he made that remark to Mr. Ahola, who of course was in awe of Bix's unique ability - something Bix himself took for granted.
As for the Tram Arcadians "panicking the town" comment - Bix was speaking on behalf of the whole band. He took pride in their collective accomplishment, and as a team player, was happy to be part of such a wonderful crew. He didn't single himself out for praise here. He was proud to be one of the "boys."