What are you going to do with the head, most bear rugs with felt also have the head mounted, open or closed mouth. I have 3 tanned bear hides that I just hang from hooks, but I could also put them on something as a throw. I have a zebra rug with felt but on them the head is ironed flat, looks good.
The rugs for bears that I do for customers have the felt and padding/backing done by a professional taxidermy rugger. There is padding, a canvas looking backing and 2 layers of scallopped felt on the edges, as well as hangers. Many customers opt for 2 layers of black felt on black bear rugs, it makes the skin look larger.