A better option might be staying
inside the park. There are a number of National Park Service concessioner lodges in Yellowstone to fit just about any budget. Some are probably rather expensive, but many are not at all.
Go to
www.nps.gov/yell and click on "Plan Your Visit" on the right side of the home page. Then look for "Lodging" on the left side of the next page. National Park lodges usually offer exceptional value -- and you're already familiar with the benefits of staying
on-site!

National Park lodging usually offers a range from tent cabins, to rustic cabins, to regular hotel rooms, to very elegant $400-600 suites. I've done all but the elegant accommodations, and I've enjoyed every one. In a park, the room is NOT your vacation, and frankly any decent place to sleep is better than staying miles away.
If you go to Yellowstone, don't miss Grand Teton! It's only about 35-40 miles south of the southern border of Yellowstone, and it's gorgeous. It's one of those rare places in the Rockies where the mountains rise right up out of glacial lakes, and it's really stunning. Teton is one of my favorite parks, ranking only behind Yosemite and Glacier on the scenic beauty scale.
The best flying destination for Yellowstone is Jackson, WY, which is just south of Grand Teton. There are regular major airline flights into there. Also airfares to Jackson are probably half what they would be to Helena or other cities out there. Except for Jackson or Salt Lake City, it's a pretty hard place to fly to.
Good luck and have a great trip.
Ranger Jim