Interesting question!

"Jazz" musicians came from quite a variety of backgrounds, so there isn't much of an archetype for their education. Many of them, especially those in large cities such as New Orleans and Chicago may have studied classical music. "Jazz" as a subject wasn't taught formally until the 1950s, so the first several generations of jazz musicians didn't learn to play their style of music through academies.

The most common type of education would have been band classes as a youngster, followed by years of on-the-job training and personal practice. This is why early musicians often possess such identifiable and unique sounds, they weren't studying from a common curriculum, and were generally adapting more "classical" techniques to the new style of music.

Hugely influential (then and now) was mentorship and private study with the master-musicians on any given instrument. It was very common for players to grab lessons with bands as they travelled through town (often this was a way into the scene). Further, since live-performance was more prevalent in those days, it was very common to be able to find musicians who lived and worked exclusively in a single place. These musicians would often give lessons, and substituted for formal study when it hadn't yet been established.

In sum (a crude analogy but one that I think is effective and correct): Think of this period of musician as being closer to tradespeople, often receiving rudimentary instruction through schools and at home, but really becoming knowledgeable through on-the-job training and practice while on the road.

Sorry for the brevity, on the road for the next few weeks with just my phone.

Composers needed role players that would follow directions, get the job done for nickels on the dollar in order to maintain operations. Due to the nature of the work and the composers reluctance to pay full price on role players and the inability of these role players to efficiently provide for their family, supply and demand presented itself. Because the economical benefits were a priority to the composer, the composer learned that hiring African Americans would provide economic benifits. African American musicians were in turn encouraged to pick up the instrument at a young age and it was important they were highly trained as young as possible, in order to enter the workforce. So the elementary school systems would provide the best musicians to train and teach them very young. Post bop was not part of the business model and the composer took a huge blow, unions were striking and the composers influence and power lessened.

The ironic take on this is that the result of the composer cutting corners, capitalizing on racial inequalities and utilizing modern outsourcing tactics allowed African Americans with highly accessible training and eduction through the school systems. Composers presented their role players with a platform of change. Composers directly facilitated their own demise because they underestimated human beings and what they were capable of.