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Staehpj1 hinted, I don't think I would like to try to see the park by bicycle. There is not really a bicycle trail infrastructure. Some of the roads, like near Mt. Washburn (sp?) are narrow, twisty and beat up. The Park Service did make a point of widening roads and the motorist started driving faster and killing more wildlife. Sad.
Yellowstone is the ultimate wildlife place. The grizzly bears are at about the carrying capacity of the region. We saw one last year. There is a wolf program supported by the Yellowstone Foundation. If you see cars in a pull off and spotting scopes set up, that is the Yellowstone Foundation wolf rangers. They know where the wolves are and they will let you watch them in the 'scopes. Wolves actually get near the roads.
I recommend hiking there, too. If you get 1/4 mile from the trailhead, the crowds drop off.
The wolves are actually in trouble because the federal government has prematurely removed them from the endangered species list. We need some action to protect them. Defenders of Wildlife:
www.defenders.org