I guess my ultimate question to you then is this:
What is your ultimate goal in contacting her, to apologize for your mistakes?
To me, if you admit it to yourself, learn and move on, I don't see how apologizing to an ex can help someone at all. To me, it's just an excuse to contact the ex. I've gone through 5 million scenarios in my head the past 2 weeks on what I can say to her to let her know I still care and am thinking about her. I'll tell you this, apologizing for when I got upset and stormed out (the last time we talked, 2 weeks ago), was right at the top of the list. Am I sorry? Yes. Is apologizing to her going to change ANYTHING between us? Not at all. Therefore, I don't see the point in contacting her for ANY reason.
But, I so thank you for your opinion. It's always good to read others views on things.