There's no way to predict how your dog might respond to a real bear. However, it's very unlikely Charlie Horse would wag his tail and beg the bear to pet him. There's a good chance he would bark a warning. Some dogs will do what they can, holding their ground, as perhaps your neighbor's dog did. Others will quietly, or not so quietly, run and hide.
Emerging from winter hibernation, bears are hungry. Experts suggest keeping trash securely closed (use bear-proof trash bins), and never leaving food out in your yard. Remove plants with berries, a bear delicacy. Some people claim wolf urine (available at some feed stores) is a deterrent.
You could dribble it around the edges of your property. If it works at all, it will only be effective until the first significant rain. While a large dog can be a deterrent, I don't recommend leaving your dog outside unsupervised. It would be wise to install outdoor lighting and make lots of noise when you go outdoors at night.