Well, I think this is a good idea. I'm always looking around for ways to get to hiking destinations without a car (I own one, but I like to keep the carbon out of the air when I can). Generally speaking there aren't that many such services, but I just read about a new bus called Bundubus. They have quite a bit of service originating from SF, LA, Las Vegas, Salt Lake, a few other places, and going to Bryce, Arches, Capitol Reef Grand Canyon, Zion, Death Valley, Yosemite, Yellowstone, and elsewhere. It seems like Las Vegas is their main hub. I don't entirely understand how it works, and service is limited at this time of year, but it increases mid April through fall It has a feature that would allow you say to get off for a few days in Death Valley en route to Yosemite, then spend a few days in Yosemite before going on to SF.
Again, I don't have any experience with them but there aren't many options out there that seem to do this sort of thing. There's Green Tortoise, and there are some places served by Amtrak. If anyone has any experience with them, please let me know.