Can I shoot a bear in self-defense? Will I face fines and jail time if I do?
For hunting bears you have to check with your local rangers for hunting season, permits and so on.
Self-defense is self-defense if your mental state does not allow you to think and you feel killing is the only way out than it the only way out.
You can. Bear spray is a more humane option; however, you do ask about legal repercussions. You can shoot pretty much any animal in self defense in the USA. After you shoot the animal it is important what you do if you want to avoid fines. Once the fight is over and you know you are safe you need to call the forest service. If you don't know their number call 911 and they can and will help you.
Source: Last year a buddy of mine killed a Mountain Lion (cougar) in self Defense and didn't have a tag for one. A guy came out and looked at the Cougar, asked some basic questions like what weapon was used. Where was he standing. Where I was. What was the Mountain Lion doing that made him feel he had to kill it. When did it happen. The last question was "Will you help me carry it back to my truck?" He filled out a piece of paper with our info and that was it.
During the carry back we asked about what happens and he told us that depending on very technical qualifications such as if he wants to eat the animal or not and how far is is from his truck determines if he hands the hunters a tag and says have a nice day or takes it himself. Also, he said that if it was obviously not self defense or he had a bad feeling about it he could get the police involved but usually doesn't have to.
You can shoot a human in self defense, so don't worry about shooting a bear if you have to. I have UK military experience, and let me tell you, shooting a moving target with a handgun is difficult. If a 400kg bear is coming at you, and you only have 5 seconds to get an accurate shot away with all the adrenalin flowing, then chances are you will not stop the bear, even if you are well practised with the handgun.
The only firearm I would consider for a CLOSE encounter with a bear is a pump action shotgun. Easier to aim and far more stopping power. Not a particularly convenient or inconspicuous piece of kit to carry when hiking! But you do have that as a legal option here in the U.S.?
But bear(!) in mind, your mindset will change if you are carrying a firearm. You may be tempted to go for the gun too readily when there is perhaps a better alternative course of action, e.g. talk loudly, avoid eye contact and move away slowly.
Still, if I had a shotgun and bear spray, I would instinctively go for the shotgun first, which may be less effective than the spray. Given enough time though, I would fire shots in the air, before aiming at the bear. I have seen u-tube videos of Grizzlys scampering away in fear from the noise of a shotgun.