We flew into Bozeman last year, drove to Idaho and was setting up camp by 1:30. Got a new Dodge, 4 door 4x4 pick up. It was a true 4x4 truck and was in good condition. It was $532 a week which isn't that bad. We would have spent that on gas driving. We don't horse around in them in don't take chances in areas we could get in trouble, but we have some ground clearance and 4X4 if it were to get snow or make a wrong turn. The towns that cater to the Yellowstone tourist usually have pick ups.
The biggest draw back to this is you have to really limit your hunting on the last day or two unless you want to change your flight or rental agreements. They own you unless you can afford the big fees. We had a big bull only rule the last two days. My son in law had to pass up a raghorn (his first hunt) on the last day. Wouldn't have had time to pack it out. Everything gets real expensive once you kill something. Plus a lot of extra work and logistics to get it home.
I prefer driving even if it is 32 hours. I may do it again, as it saves 3 days of driving, but having your own schedule and all your gear is nice. I guess if you don't kill anything it works out great...I want meat on the ground.