I've not experienced this situation in a relationship, but I have to say, some of my friends can't drive and it is very rare that I am bothered by having to give them a lift. As long as they don't bug me to drive them places I am often happy to oblige. I understand that not everyone can afford to, or wants to learn to drive.
The only situation that is annoying is when I have to drive us somewhere to go out and everyone else gets merrily pissed and keeps pressuring me to drink. I absolutely refuse to touch alcohol if I am driving and to have them hassle me is irritating. Do they really want me to join in and get pissed and then jeopardise our lives on the way home? So long as you don't get her to drive and then revel in getting pissed in front of her, it shouldn't be a problem.