Willie,
Keeping in mind that bears rarely attack people, and that (especially in a Cessna 140) the weight of a firearm is likely to be more dangerous than going without, here's what I know.
Accuracy is everything. A .50 BMG round won't stop even a small bear if you don't hit a vital area. THE important factor in a defensive round is whether you can hit what you're shooting at, under stress, every time. The one and ONLY recipe for accuracy is practice, so while a winchester .458 magnum may be the ultimate bear slayer, it's a poor choice unless you have the money and physical stamina to get REALLY good with it. That means hundreds of rounds every year in a combat setting, not twenty rounds at the range from a rest, followed up by another five every other year to make sure the sights haven't changed.
A 12 gauge slug is a fantastic round for bear defense...I'm less thrilled (wouldn't trust it against a brown bear) about buckshot, as the penetration is not nearly as good, but some like it.
I think that a 12 gauge shotgun is the ultimate survival firearm for a lot of reasons...chiefly among them being that the firearms are easy to shoot, cheap to practice with, inexpensive to acquire, and incredibly versatile.
The same gun which will stop a bear will, with equal efficiency, put a grouse, hare, or porcupine over the campfire coals. Buckshot will (I'm told) harvest salmon with ruthless efficiency so long as someone is downstream to scoop up the corpse. In a survival situation there isn't another weapon that even comes in a close second to being able to feed and protect a person. About the only disadvantage is that the shells are fairly heavy and bulky.
One of the all time best guns I own is a Stevens side-by-side 12 gauge that I bought at a pawn shop. While I was there I bought a hack saw and a miter box. I cut the barrels down to 18 1/4 inches and have been using the gun for the past twenty years. Cutting the barrels down did very little to the pattern...it'll still put all 12 pellets of 00 buck in a human target at 30 yards...24 pellets if you want to pull both triggers at once. With slugs I can hit a gallon milk jug at 20 yards with monotonous regularity.
Two rounds isn't the ultimate in bear protection, but with two triggers I can load one barrel with a #8 dove load and hunt grouse in thick alders, knowing that the second barrel is loaded with a 1 1/4 oz slug. In twenty years I've never mistaken one trigger for another. Also, a double barrel gun has a very short action, making it a good three to four inches shorter than a pump gun.
I also have a Remington 870, which is probably the most tested, most trusted, most reliable pump shotgun ever made. It's also about as romantic as a Cessna 172, but utility has it's own appeal.
About the only thing you really need to stay away from are the pistol grip shotguns...they look cool but are useless when you try to hit anything with them.
What any 12 gauge shotgun will do that no other weapon will is both protect you and feed you, providing you learn how to use it. Obviously you also need to do some research and learn what rounds will do what...try shooting a rabbit with a slug or defend yourself agains a bear with a low brass #8 and the results will be comical/tragic.
Bear in mind (pun intended) that there is no shortage of bad advice on the web. I've seen firearm advice on this forum which was so off base I was unable to write a civil reply. If you choose to protect your life based on the suggestions of some unknown person in cyberland, well, good luck. Any fool can carry a gun, but knowing how to use one takes thought, time, effort, money and dedication. Unless you're a shooting enthusiast and find joy in the process, the chances of actually having to put that skill to work are so slim that it's hard to find a justification.