1) When Bears Hibernate do they travel higher into the Mountains to do so? It seems that people have seen/taken Bears in higher elevations.
Regardless of where they hibernate, bears are going to be where the food is. Depending on location that could be wild onion, flowers, grasses, berries, etc. Find the food sources and look for sign.
2) Is it still a little Early to see Bears? I thought with the descent weather we have had lately they would be active.
Active is subjective. Early in the spring they are less likely to travel very far as they are often still lethargic. Find the food source and you will find sign.
3) To call Bears in, Do you wait till you can see one? Or Do you sit down glass a bit then let'er rip?
On the westside nearly all of my calling is cold calling over or near food sources. On the eastside I would cold call if there were parts of the terrain that I could not completely see or if there was a lot of cover for a bear to hide in.
4) I heard that Bears are attracted to Gun shot. If I shot a coyote would a Bear come to or shy away?
I have only seen a couple black bears not leave at the sound of a rifle shot and they were a couple hundred yards away. I won't shoot a coyote on a bear stand unless I plan on ending the bear stand.