Brad and I have have interchanged a lot of ideas regarding the concept of genius. I think the dialogue was stimulating, productive, and it helped me clarify my ideas on the subject. Brad and I (I hope I am not putting words in your mouth, Brad) agree that Bix was a genius. So does Randy Sandke who titled his essay on Bix's music, "Observing A Genius At Work."
Genius cannot be measured quantitatively. There is no ruler or scale or meter that allows us to measure genius. Therefore, I cannot provide documentation that demonstrates objectively that Bix was a genius. By necessity the assignment of the word genius to an individual is a subjective call.
What I can do is bring up various definitions of genius and show that Bix conforms to them.
From Britannica. "Genius is distinguished from talent, both quantitatively and qualitatively. Talent refers to a native aptitude for some special kind of work and implies a relatively quick and easy acquisition of a particular skill within a domain (sphere of activity or knowledge). Genius, on the other hand, involves originality, creativity, and the ability to think and work in areas not previously explored—thus giving the world something of value that would not otherwise exist."
"New ways of describing genius nearly always incorporate ability, creativity, mastery of a domain, and other personality traits such as autonomy and capacity for endurance."
Brad likes this definition of genius.
James Lincoln Collier's in his fine book, "The Making of Jazz." In his chapter on Louis Armstrong, Collier writes:
"... I take the word [genius] to mean somebody whose accomplishments are beyond analysis."
"With the ordinary artist, we can discover in his background and character where he drew his material from; with the genius, we often are unable to determine how he arrived at his startling conclusion. Armstrong's melodic gift was simply astonishing, and there is no explaining where it came from or how it worked its magic."
The recurring theme is originality, creativity, our inability to understand how the genius comes up with his/her creations, the fact that works of art, science and/or technology created by geniuses would not exist if the genius had not been born. By all these, let me call them criteria/diagnostics for lack of a better word, Bix was indeed a genius: his originality and creativity were unique, the source of his creations remains a mystery, we cannot explain them by using precedents. That is my view of Bix as a genius. Others may disagree with my calling Bix a genius. Then it is incumbent upon them to provide evidence about what characteristics of a genius are absent in Bix's work as a musician.
I agree with you: the word genius (like the word hero) is thrown around with little understanding/discirimnation as to what it really means. In my 77 years of life, I only met three geniuses, one older than me and two younger than me.