I can understand some of the frustrations of being called up close to the end of the jam. But it happens.
Usually the guy running the jam wants to see a player do his/her thing when the place isn't full so they can see what their talent level is.
There's a great open Blues jam here in DC. When I first went there, I didn't get called up until close to late. When I got to play, they were impressed and I usually get called up early and often after they figured out that I knew pretty much every Blues groove known to man. I also spent time talking to them, and since they were Blues geeks like me, we got along well, which helped.
For a good jam, the guy running it will try to match players optimally, so sometimes they may mess with the order. For example, there were a couple of younger teenagers at the jam one night. They got on early, and they brought in me to play bass and sing, and another good drummer up there to hold things down for the kids. We had a good set. The guy running the jam apologized for putting me up with the kids, but told me he trusted that I could keep things together, so that's why he did it. He also does stuff like bring in a new bassist with a regular drummer, or keep a hot rhythm section up for more than a couple of sets. He's trying to keep the best group of players up there for the longest time, so that the audience is still entertained.
For the Blues jams, if it's run well, and you're patient, not easily offended, and play bass well, you'll have plenty of opportunities to show your stuff.