You can do a post-bac course anywhere, such as a state school. You are under no obligation do it at one of the more expensive places such as Bryn Mawr, Scripps, Goucher, etc. Also, there are a few public schools that are known in particular for being favorable to post-bacs: Hunter in NYC and Temple in Philly are two that come to mind.
But you also might want to think about what "affordable" really means. I decided for instance to go to a more expensive post-bac at a private school. It's true that it will cost me about 25k, instead of maybe 10k at a state school. But I think I'll get better advising, smaller classes, etc. which will improve my odds of eventually getting a seat in medical school. And that's the ultimate goal.
Medical school itself is likly to put me 200k into debt; what's 25 or 30 grand more in the scheme of things to get myself started down the path right? Furthermore, I'll finish my post-bac, if things go according to plan, in just one year, after which I'll have a good chance of linking directly into a med school. That means that I'll be starting my residency in five years, instead of 6, 7, or 8 if I took a longer time to do my post-bac work and/or couldn't link. Following the logic here, starting residency 2 or 3 years sooner = finishing residency 2 or 3 years sooner = I will ultimately have 2 or 3 more years to practice medicine and earn a physician's salary. When you consider that, the 25k or so really pays for itself in the long run.