This bear is probably nothing to be concerned with. In CO they den every winter. it is mid Nov and that animal will be denned up before Dec. Then he/she will sleep through the winter. When it wakes up in the spring it is going to be interested in getting grass and vegetation into its system and not messing with you or a dog.

I grew up in CO and spent a huge amount of time in the wilds. Sometimes with a dog by my side, sometimes without. I saw my fair share of bear and I never had one act aggressively. Most the ones I saw were busy getting out of the area. There are really only 2 instances where I would be concerned.

#1) A sow with cubs in tow isn't something you want to fool with. Get between her and the little ones and you're in serious danger. Problem is, cubs are curious and sometimes they get into trouble. This scenario is where a dog can get you in trouble. If a dog screws with the cubs, Mama bear is going to go after it. Dogs will flee danger and head to where they fell safe, which is by their master's side. So, the dog could actually bring the bear to you. This is why it is very important to keep your dog under control. Bad idea to just let them roam free.

#2) Bears looking for food before den up can get in trouble. All they think about is filling their bellies during Sept and Oct. They need over 10,000 calories a day. So if food is around, they will get into trouble. This is why many areas require "bear proof" containers or insist an no food being present. it doesn't take much either. A greasy BBQ grill will bring them in.

If you are going to live in bear country, there are some responsibilities you need to take. As to whether you could shoot a bear going after your dog, you might be able to get away with it. But I wouldn't want to try it and find out. CO is very, very serious about game violations and that one could go either way. Better to just be smart about the bears in the first place. After all, they were there before your house was built.