Just apologize and own up to your shit. That would be the mature thing to do. Demonstrate that her value is more important than your ego. That’s what separates a boy from a man.
As you should. If you’re ONLY an asshole to a girl, she’s either not going to think you’re interested and/or she will never get the hint that you’re interested. You gota!
I think showing a little vulnerability and interest is a good thing. If you follow that with playful jabs (not literally) and you pair it with hot and cold behavior…. She’ll probably remain interested. You did good, boss.