Mike, I think if you took a head count here..You would find the vast majority started to play in public....with a group of some sort...For ,the old accordion players, it was by design that we were part of accordion bands, for this purpose...many times the accordion bands would perform in showcases[even TV]...This contributed to our individual confidence..
Some of us went on to play in small combo bands with drummers, Sax players and maybe bass and guitar players...the point as you touched on...we were not alone..
This can be continued by maybe working with a vocalist..in my case I chose to work with young female vocalist,,this really helps because , believe me you are not the center of attention in this situation...
It will all come about ,when you will feel totally comfortable by your lonesome...great tools[keyboards] will also help in this respect..