The folks at the Gunnison River Pleasure Park, the takeout, run a shuttle service. They will go with you (in your car) to the put in and drive your car back to the takeout. You need four wheel drive or at least high clearance to get in. It used to be $50 but it may have gone up and I don't know if they run this time of the year.
They're in Hotchkiss - (970) 872-2525
My experience with them in the past is that they hire some of the older local guys who have provided some colorful conversations on the way to the river.