My best advice would be is be the bigger person and sounds like you were You reached out and wanted to fix the problem and now it's the girls problem for why she doesn't want to make amends. It's her problem not yours. If its really bugging you maybe you both could get your school councilors help to solve whatever the issue is
Believe it or not, she has low self esteem. When I was in school ( many moons ago ) , I was bullied by this girl and after a while I would just look at her like I felt sorry for her and would wait until she finished her little tiraid and ask her if she was finished, shake my head and walk away. After a while, when she saw she was not getting the expected response from me, she stopped. People also tend not to bully people with their friends around
Yes, ignore her, but that isn't always easy. Try coming up with good comebacks (also not easy). Talk to your parents, the guidance counselor, or someone you trust for help. Maybe, you could talk to the girl honestly and ask her why she is mean. Talk to her and maybe she's just scared or bullied on herself. Be nice and kill with kindness. Offer her help and compliment her. Just try not to let her get to you. Good luck!