Kaylee,
This may be about the last thing you'd choose, but I've done some thinking about this subject, since I plan on finding myself up in Alaska. For you, your needs are a light, fast-handling, compact firearm that is so portable that you'll never leave it in the plane or cabin. If it's sturdy, easy/fast to build up, and reasonably lost cost, those are all pluses, too.
Even if it's not a phased-plasma rifle in the forty watt range, with a purty wood stock.
For close range bear
defense, an 18" GR Mossberg or Remington with an M4 stock, loaded with slugs would be dandy. This'll give you something almost as handy getting into and out of cockpits as a pistol grip version, but with the added goodness of shoulder-mounted fire. Add a sidesaddle, and you have 4 or more (depending on model) extra shells that stay with the weapon.
If you only wanted "just one" weapon, that sidesaddle could be holding #6 shot.
(Or pepper loads?)
You
could also mount a light, on the barrel or integral to the slide. Night-time defense against dangerous game is perhaps the most legitimate use I can imagine of white weapon lights.
John