Just tossing my two cents in. I think if it were me, I would be so curious at this point that I would meet with her just to see what she was going to say. I would be prepared to get up and leave, though, if it started to go downhill. I would definitely try not to get my hopes up that this was going to be any kind of "restart" but rather approach it almost as an anthropological investigation, if you know what I mean--"Hmm, interesting, what will she do now?" without being emotionally invested in one outcome or another.
As others have said, you deserve an apology, an explanation, and much better treatment from now on if this woman is to remain a friend. If she doesn't feel she can remain a friend, you still deserve at least a sincere apology. If you don't get even that, I would suggest remaining at "friendly acquaintance" level, and that means you don't have to go out for coffee or anything else with her in the future.
However, I would not blame you at all if you decided you didn't even want to meet with her now and canceled the meeting--that wouldn't be considered rude in this case, would it? And didn't set up or commit to another one. As others have mentioned, she could start by apologizing through email if this was really the purpose of the meeting... "Just wanted to let you know how sorry I am about the way I've acted lately. Can we get together so I can explain and apologize properly?"