I got in without a Bachelor's degree, or an Associate degree for that matter. I have actually called schools, and nobody really cared (except TCOM). FWIW, I think I'm the only person in my class who doesn't have one.
Basically, I should be a year behind where I'm at now, but I went ahead and got as many pre-reqs done as I could, took the MCAT (without having taken physics actually), did reasonably well, and applied with somewhere around 100 credit hours. I had no problem getting interviews, got an early acceptance and a scholarship, and said to Hades getting my degree. (Actually, my school was cutting out my program anyways. They no longer offer my degree... well, what my degree would have been. 🙂 )
After my acceptance, I called and told them I would have all of my pre-reqs done, but would not get my degree. They didn't care at all. Basically, I would have had to continue a monstrous load of classes right thru the start of med school orientation to graduate, but I needed to make some money because a nino was on the way. My school was very cool about the whole thing.
Moral of the story: it is possible. I would caution not to listen to people that have not tried to apply without a degree. However, I would also caution that no degree definately = no sure thing. Good luck.