Key statements:
-You offered to do the work, she didn’t ask you to. I’m betting that you offered up your car too.
-The violation is a result of your negligence and not hers.
Just because you were doing a good deed, doesn’t mitigate the fact that it is ultimately you who did not make the car road worthy. It would be courteous of her to pay the ticket since you were doing her a favor but that is her option not yours.
Man up and pay the ticket... Honestly, you would do a disservice to your masculinity by making her do so.