I spent 45 minutes yesterday morning writing you a response, and then it disappeared into the void! Very annoying. Anyway...
There's more that you need to know on this subject than you are going to get in few posts here. You should get copy of the best book on the subject, Bear Attacks: Their Causes and Avoidance, by Stephen Herrero. You might also be interested in Alaska Bear Tales, by Larry Kaniut.
Only a brown bear is going to be big enough to get its jaws around your head. Even then, it would need to be an unusually large bear. The only place that you're likely to encounter them that big is Alaska, and even there, that would require a larger than normal bear. It happens, but it's not something you need to worry a lot about. I'd be much more concerned about a bear decapitating me or eviscerating me with one swipe of the paw, or biting my face off, than clamping it's jaws around my skull.
Bears can run 35 mph, much faster than a human. Thus, running is probably futile. Worse, it can can trigger an instinctive predatory response.
Guns tend to be a poor choice for bears, and especially brown bears (grizzly bears), for several reasons: 1) bears have thick skulls, and bullets often bounce off or lodge in their skulls before reaching their brains; 2) bears have tough hides and thick fat layers, which often stop bullets before they reach vital organs; 3) brown bears are so tough that they are likely to continue attacking after they have received several fatal gunshots. If you do try to shoot a charging bear, you're supposed to aim for the clavicle (the front of the shoulder), to stop the bear's ability to charge. Good luck.
Bear repellent (pepper spray, but not the same as the little cannisters you get for dealing with people) is considered a highly effective method of of deterring attacking bears.
You need to be able to tell the difference between a black bear (Ursus Americanus) and a brown bear (Ursus Arctos Horribilis), because they have very different behaviors. Despite their names, either kind can be either black or brown, or even blond, or sometimes auburn. Besides the fact that brown bears are much larger than black bears, there are numerous tell-tale differences. Brown bears have much larger claws, which visibly protrude out of their paws, as long a fingers. Brown bears have a prominent shoulder hump which blacks do not. Brown bears have more rounded ears, set wider apart. Brown bears have a more scalloped snout shape than black bears.
When black bears attack people, it is likely to be either an adolescent newly on it's own and experimenting, or a very old or sick starving bear, thinking you look like easy pickings. Black bears attacks should be assumed as predaceous; and you should certainly fight back against a black bear that hopes to eat you. Also, black bears are usually rather timid animals, and are likely to back off if they meet a lot of resistance.
Brown bears rarely attempt to prey on humans. When they attack, it is generally because they see you as a threat, and they feel the need to defend themselves. Thus, fighting back is going to make the bear continue to perceive you as a threat. Don't even look at it's eyes, which it could perceive as aggressive. With brown bears, you are supposed to play dead. By doing so, you can often convince the bears that you are no longer a threat, at which point, they'll leave you alone.
There is a particular posture that is considered best for playing dead while experiencing the brunt of a bear attack. You should kneel down, lean forward and tuck your head against your knees, and interlock your fingers behind your neck. This exposes the muscles and bones of your back to the bear, instead of exposing your vital organs.
Of course, what you should really try to do is prevent a hostile bear encounter, in the first place. Learn what sort of areas are likely to attract bears, such as berry patches and fishing holes and bear trails, and stay away. Learn to recognize their footprints, tree markings, feces, and other signs, and learn to tell how fresh they are, to know when you are entering an area with a brown bear (at which point you should leave immmediately). Make sure to make enough noise that the bears can hear you in advance and have time to leave. (Surprised bears are likely to feel defensive; alerted bears would usually rather leave and avoid trouble.). Make sure your camp, clothes, and sleeping gear have no food scent. Also, understand the circumstances that are likely to make a bear feel especially defensive, such as a mother with young cubs, or a bear at a carcass. Stay in a group of several people; bears would almost always choose to flee rather than attack a group.
Remember that these are just generalizations. Bears are smart animals with their own personalities and behaviors.
And to end with a joke: How do you tell the difference between a black bear and a grizzly? When you climb up a tree, a black bear climbs up after you, while a grizzly knocks the tree down.
