I don't see an issue with you walking your date to her car.

My advice, based on little knowledge of you, the situations, and who you attract, is to be straight forward with what you want. Don't be blunt. You must still be respectful in your approach. Absolutely do not waste anyone's time beating around the bush though.

If you can muster the bravery, ask to take her out on a second date at the end of the night. If she says no, move on.

I say all this with the hope that you are reading her nonverbal signal throughout the night too.

BUT WAIT THERE'S MORE!

Make sure you get to know now what she wants out of all this (one night stand, fwb, a serious relationship, Etc). Like men, women have a motive for their actions. Knowing her intentions allows you to have realistic expectations. Overall you will have a less painful experience.