If you want a remote area without a lot of crowds, try the Shoshone Lake trail. Its in the southwest corner of Yellowstone, about 11 Miles in, and beautiful country.
Firearms are forbidden in all National Parks, so definitely keep this plan to yourself.
The pistol you are going to carry should do the job.
I went in this same trail many years ago with a group of Boy Scouts. We stopped on a sandbar in a creek about halfway in, and when I went to the upstream end of the sandbar, there were several HUGE grizzly prints there with the water still running back in them.
We never saw a bear, but were very careful about not eating or having food within 100 feet of our tents, and not allowing things like chap stick or toothpaste to end up in the tents. Evidently, "scout" was not on the menu.
We saw elk, mule deer, a badger, eagles, osprey fishing in the lake, al sorts of stuff. And lots of footprints, bear poop, both black and grizzly. The bears probably saw us, but we never saw them.