Lighthawk - how did you degrease the hide? Yes bears are greasy, but so are raccon and beaver, both prime furs.  Dish soap, borax, Coleman fuel, lots of different things folks use to degrease. I like borax because if I use it while I'm fleshing the dry powder gives traction on the slime.
OP - you really need to work on your family's response to seeing a bear. RUNNING is the wrong response to any predator encounter, even  a growling dog! 
We see bears all the time when visiting my inlaws in Va., and they are moving in around us here in Ky.   My kids and I have seen them many times. I take my youngest by the hand to calm her, and talk in a low voice, sometimes to the kids, sometimes to the bear. We keep bear pepper spray handy when camping or hiking. Dogs are a double edged sword - bears hate them and dogs can actually get them riled. Some folks will say bears seek them out to confront if the dog is in their territory (I dunno).