I play regularly at a jazz jam. Somehow, any time something I like and over which I could solo competently (for an amateur in rural England) appeared then either the bass solo would be forgotten or someone else would play over it, etc. etc. If it was an unfamiliar/complicated piece I'd not fancy risking then the chance of a cry of "bass solo!" and everyone stopping to listen would increase. I think this is mostly fixed now, though.
What makes the session go well is communication. Things are usually fine when someone clearly names the piece and the key (the actual key, not the first note of the melody or root of the first chord)*, explains any special arrangement they want, waits for those who require them to find the iReal charts or real book, then clearly counts everyone in* rather than simply starting to play and hoping everyone comes in.
Probably a lot easier at a blues jam, but paying close attention to the form and where we are in it is something that improves the performance no end and is often neglected.
* Guitarists...