OP, I don't blame you for not wanting to walk another 20 minutes back to the bar to meet your friend, and I don't blame you for the night being ruined. Honestly, I'd be upset too and I think in the first phone call, you handled it just fine. You were annoyed, sick of walking around, and just wanted to go home and have some time to cool off rather than talking about it right then - especially in public, on a train. I don't think anyone is under an obligation to let someone else fix a problem they created - sometimes, you're disappointed and hurt and just want to go home. That doesn't mean this was a malicious or rude thing for the friend to have done - it was clearly an accident that she tried to make better. But, there was a mistake, OP was upset, and she just wanted to go home. I don't see either of them being in the wrong in this situation. Friend tried to fix it and apologized, OP just wanted to go home by that point in the evening. Neither of them, I think, were being rude or behaving badly up until this point.
However, I actually think the friend was rude for continuing to call. When I get upset, I know that it's best to have time alone to cool off, so I do exactly what the OP did - I explain that I'm upset, I need some time, and that I would get back to that person. I would be really, really unhappy if someone ignored my clear request for time to calm down and instead barraged my phone with calls. Not okay, in my book. Yes, friend was just trying to apologize and salvage the evening, but good intentions don't excuse someone from ignoring an explicit request to be left alone for a little while. But, remember OP - you asked to be left alone. Of course your friend hasn't texted you since then. Also, if she was having problems receiving texts before, there's a chance she never got the one you've sent more recently.
So, since this is a close friend, what I would do if I were the OP is not apologize. I don't think OP did anything wrong. But, in order to smooth things over, I would call - actually talk to her, don't text or write a letter - and thank friend. Say something like, "Thank you for trying to fix the mistake. I know it wasn't intentional, I was just upset that night and really just wanted to head home. I appreciate your patience with me when I needed time to cool down."