Thanks for all the comments! They are really great!
I would try the "question-and-answer conversation style", just repond with simple answers, given the charater of this colleage, she might not get the hidden message, but at least I don't have to keep up with her endless topics.
you are too nice! You shouldn't let her take the carpooling for granted! There should be some quid pro quo in effect here.
Lay down the rules. You drive the car, you lay down the rules. "Ie: i prefer to focus on the road for our safety. you can chat all you want, but i can't promise we arrive to the destination safetly if you want me to hear all you have to say, it distracts my driving."
If she can't abide by it, diss her.
The thing is that when I was in someone else's car, how do I know if I should chat or be quite? Sometimes silence just seems so weird and awkward. In your case, chatty is not good neither.