I worked a summer in Yellowstone. Roads are not bike friendly but they are doable, just narrow. As for bears, don't cook by your tents, DO NOT store food or things like toothpaste in your tent, the park service provides "bear boxes" to store food in. Use them and you will be fine. Truthfully most animal attacks in Yellowstone are by Bison, and Bison often use the roads as trails, although this is more likely in the winter. Biggest thing to watch for is if you come up on Bison on both sides of the road. You do not want to get between a mother and a baby. Make sure you stop and talk to the rangers as you enter the park they will give loads of good advice.