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Text her and say "I was wrong and you were right. I'm sorry(her name)!
I'm not sure about that. That's just going from being an asshole to being a pussy.
I think that between us guys you should recognise that you fucked up here and that you shouldn't have treated her the way you did. However, I wouldn't admit that fully to her. The apology you
should be giving by rights would be something like this:
"I'm sorry, I shouldn't have got angry with you, I realise that you did nothing wrong and that I was just getting butthurt because I'm insecure. I shouldn't have taken that out on you and I apologise".
That would be fair, but would probably result in nothing more than "well thanks for your apology, see you later".
Your only way of getting back in the game here is to say something like:
"hey, I have the feeling I might have been a bit rude to you when we last spoke, I've been under a lot of pressure lately with (work, family, insert any excuse that might be plausible), what's up with you?"
You're kind of acknowledging it but kind of downplaying it. Her likely response will be something like:
"well yes, you were kind of rude actually - as I recall you said something about not wanting to get to know me?"
Your response:
"Wow, I really said that? Shit, I didn't realise quite how I was acting. And it goes without saying that I didn't mean what I said"
Her response:
"Well I found it quite hurtful"
You: "Well yeah I can understand that, listen I'm sorry I acted that way, why don't you let me make it up to you sometime?"
Her: "Well I don't know...."
You: "I do want to get to know you cos you're a great girl and I'd hate to miss the chance"
Her (probably): "Well I'm going to such and such this week, maybe you could come along..."
You: "Yeah that'd be good"
etc etc etc
This may sound manipulative and it probably is, but I just don't think offering a straight up apology will work. You've got to give her some sense that she has "educated" you about your behaviour and that
she has been the one who prompted you to change. So my advice for now is to kind of get it but not quite. Let her help you the rest of the way.