I don't want to give my coworker a ride
Is that what you really want to do? Why don't you want to give your coworker a ride?
Because I feel like she doesn't like me and I don't like her either
Co-workers don't always get along and you don't have to do them favors if you don't want to. It is okay to refuse as long as you are polite since you still have to work with them.
I guess. I just don't feel like dealing with her
That's okay, and wonderful on you for trying to stand up for yourself! As long as you are both on amicable terms, you should be able to work peacefully and without problems.