I used to bully someone and now I'm in a relationship with her.
Is she okay with dating you after you bullied her?
Yes, that's my fear about staying with that girl.
Your fear may be misplaced. If something about your relationship worries you, discuss with your partner.
I don't want to break up with her because I love her over anyone else.
It sounds like the bullying is in the past and that's great. But you should still talk to her about it if it's worrying you, and make sure she knows she's safe with you now.