I talked to the bear biologist and the local ranger station for the area I am planning to hunt. Both were helpful and glad to talk.
They said some of the roads are usually opened on May 15 and the others clear depending on the weather. They don't plow any but the main roads. Both thought the last week of May would normally give me a good shot at having some clear roads to walk and the bears still be active. Some higher roads don't open until July 1.
Since I can be flexible, I will check back with the ranger station to see how the roads look as it gets closer.