I wear my fitbit all the time. I have never had it track mileage when I am driving. Your body is generally stationary while driving and since fitbit isn't GPS oriented this should not be an issue. I am sure Fitbit staff can explain it much better than I did but mine tracks my mileage accurately. Love my fitbit!
As far as I have noticed after having it for almost 2 weeks, the One doesn't count steps, distance, or altitude changes (that's how it tracks floors climbed, 1 "floor" = 10 feet up) while in a vehicle.
I just got my Fitbit One, and it tracked thousands of steps on our trip to Disneyland today (June, 2014). The car was a smooth ride, too. There's a couple workarounds, but it will entail remembering to either log driving as an activity and the amount of time or else getting the Drivebit app and using it.
I had one bsck in June for a week. I ended up returning it because it would track hundreds of steps every time I was in a car. And it wasn't a bumpy ride or anything. It did the same thing when I was flying on a plane and all I was doing was sleeping.