Not sure how long it would take. As far as the pelt, in the spring the pelt would be the best just after they emerge, before they have a chance to start shedding. A fall bear would have a great pelt and be better to eat, but probably harder to hunt.

As far as not eating something because of what it eats, chickens and turkeys (that aren't grown in a warehouse somewhere, eat bugs, including maggots! Ever eaten chicken or turkeys or their eggs from free range birds?