There are good and bad things about both possibilities. Personally, I'm doing a do-it-myself postbac at a state U and wishing I'd gone to Bennington. I'm 40, so your experience is almost certainly going to be different from mine.
If you go to a structured postbac program like Bennington or Mills or Goucher et al, you can expect to go through a competitive application process, pay a great deal of tuition, and land in a small class of well-supported students. The premed advising and financial aid should be solid, the volunteer and research opportunities should be great, and there should be good MCAT prep and support during med school applications. Any one of your professors should know you well enough, due to small class size, to give you a LOR. Any one of these expectations could fall down, but these are the expectations.
If you go to a school that doesn't have a postbac program, you can expect to need to define yourself to the administration so that you have access to advising and financial aid, and so that you can register for the science classes that fill up on the first day of registration. This probably means you need to apply to the school as a postbaccalaureate non-degree-seeking student, and the school will likely prefer that you sign up for a degree of some kind (a second bachelor's) so that you are easy for the school to handle. Getting financial aid without being in a degree program at a big state school isn't likely. You may or may not have more opportunities for volunteering and research at a state school, and you may or may not get to know professors well enough to be recommended.
The state school I'm at is packed to the gills with competitive undergrads who are pre-grouped-up by dorm or greek or cultural identity, and the anonymity is stifling. The line after class to talk to a professor (there are no office hours - we're expected to see TA's) takes a good half hour. I am extremely outgoing, and everybody seems to know who I am, but I barely know anybody in the thousands and thousands of lecture-hall-dwellers that I've been in class with. I don't recommend this particular huge west coast research university and I made sure my nephew doesn't enroll here.
I would have had to leave my state to find a private school with a premed postbac program, which at the time seemed too much to ask given that I can walk to the huge research university. I thought I'd save money and that I was too mature to need all the hand-holding of a structured program. Wrong on all accounts.
That's my experience. Best of luck to you.
