I think in addition to apologizing you should explain just as you have here.

I think you should try and dig up the most honest explanation of your behavior, based on your past, explain it to them inperson and then give them space and say hi in a week or two. Other than that, you'll just have to see how things go.

Shit like this is going happen in life.

Go for that lunch and make the best of it. Be honest that you enjoyed talking to her and it's unfortunate you didn't have more time.

Don't let your shitty feelings ruin her day.

It's not necessarily over, get her Facebook her number whatever. Keep it fun and accept what is happening.

You gotta detach and do your own thing for a bit. Nothing sassy, bitchy or negative. Just get your own space. Maybe she starts coming back to you maybe not. I would recommend to avoid anything chasing/controlling. Otherwise probably best to let it go.