there is one in beaver mines that the locals talk about. stella's i do believe. right across from the general store.
the other one that i can think of is on the right side of 507 just after you turn south from hwy 3.
you could also try the castle mtn hostel. they do have private rooms and you have great access to the castle, lynx, carbondale, gardner, lost, suicide and york. of course all those rivers are now closed but a thought for next september. i have a friend that works at the resort, and he also guides.
i have not frequented a BB down there. sorry. i sleep in my truck or at the resort.