I've worked with loads of musicians who don't / can't / won't drive, and they all fall into different categories.
Some of them assume they're making their own way unless offered a lift, and are extremely grateful when that happens.
The worst ones are the ones who half-expect to be picked up and dropped off by someone else, for petrol money or 'a couple of drinks', forgetting that the driver has to leave earlier, get home later, and pay a chunk of money for having a car in the first place.
Good luck to any drummers out there without a car...
(I appreciate life is different in central London, etc. so the above doesn't apply)