Parking at the top can be tight for a big A and toad. I agree to leave the A behind and just drive the car up. The road itself can be done - the unpaved section will depend on when they last graded it - but you aren't going to want to deal with parking and turning around.
brochure for Bodie - at the end of the brochure, there is a map of the town. You will have to park parallel along the edge of Bypass Road. It is a narrow two lane road. You will have to turn around to leave. The parking lot is for cars and won't fit your rig.
It's very scenic out there, but the towns are very small and limited (as in fuel, supplies, etc. - what you will find will be more expensive also).
Be sure to visit Mono Lake - hopefully the water level is up from last year.