Hi, Ev. Welcome!
Yes, birds love to use pet hair in their nests. Undercoat on retrievers appears to be their favorite type, but they use our setters' hair, too, and probably won't turn up their beaks at a chance for some cat fur!
If there's enough (as there is with our setters), we pack the hair into clean suet cages or some sort of mesh bag (like the sort that fresh produce is sometimes packaged in) -- it's a lot less complicated than trying to pin it to the clothesline. The birds love pulling it out. We've even had hummingbirds entertain us as they try to steal a particularly attractive bit of fur and fly off with it.
You can start any time--most of the migratory breeders won't be in your area for another month, but the chickadees and nuthatches will appreciate it now. We usually offer it right through May, but traffic falls off once the nests are built and the eggs are laid. I do put any leftover hair out in July because goldfinches are very late nesters and might be interested, but I have to admit I've never caught a goldfinch taking any....
As for bears, the hair shouldn't attract them at all if that was a worry for you. I have to bring in all my seed, suet, and jelly feeders every night in the summer, but the bears aren't interested in the hair cage at all, so it stays out. The raccoons don't seem interested, either.