Sure you can, YNP is roughly 40 mi east-west by 50 mi north-south. Most of the near sites are at least 10 miles from the Fishing Bridge CG, some are 20 miles or more and that's the crow fly distance. Pack a lunch before you leave. If you camp outside the park you can double those distances.
Bison can be avoided just stay 100 ft or more away from them. Grizzles, especially females with cubs are more dangerous if you cut cross country. But incidents are rare especially if you don't do stupid things.
On a more serious note there are a lot of long trails but you'll need transport to get you to the trailheads.