I'd let her stew in her own evil juice.

Seriously. People who want to hate will hate. You can still have a good day. I say just ignore her. If you don't think that is possible, a cool "good morning" or "good afternoon" or good evening" is all that is required.

I don't believe anyone is superior to anyone else. <--that is one reason why people hate me. And it doesn't bother me a bit