I got to do this (kinda) for Steve Kilbey of The Church this spring.
I say kinda, because he didn't need chaperoning (he's been there, done that with the rock star thing), just chauffeuring, and because it was only for a couple of days, not a week.
We travelled between tour stops, so we spent several hours in the car each day. He was a remarkably good travelling companion. I always enjoy talking to Steve anyway, so this was just like an even more prolonged conversation. I'd transport him again any time.