You should sue her in small claims court. You dont need a lawyer or anthing like that. Small claims court exists for stuff like this - disputes about small amounts of money. The procedures etc. are different everywhere, so you should do a search for wherever you live and 'small claims court' to find out the specs on how to do it.

It sounds like you have the evidence you need - proof that you paid for a ticket she used (your credit card statement) and proof that she knew she had to pay you back (her texts and stuff saying she would).