If I was going to Alaska I would pick up something there and bring it back as a memento.

Glock 20 in 10mm FTW.  15 rounds(cross your fingers) of full power 10mm is potent.

I forgot to mention this earlier but my father did say when he dies I get is .45 1911 but hopefully that won't be for another 20 years from now.

So I will probably end up making a 10mm unless the special parts are significantly more expensive.

Quality 10 mm barrels are probably a little more that quality .45 barrels.  GI style aftermarket or take off .45 barrels can be significantly cheaper.  You get what you pay for.
 
The 10 mm slide will cost quite a bit more than a .45 slide, since there are lots of "surplus" and "take off" .45 slides available online.  That being said, you won't know how well your frame and slide will mate unless you have it in hand or order a fitted pair (again, $$$).  Also, know what you're looking at, and look carefully--is that a scratch or a crack?  Is the firing pin hole properly sized?  Concentric?  Are the lugs worn?  Etc., Etc.  Don't buy anything unless you can return it after inspection. Be prepared to eat the return shipping (that's fair enough, to me).

Magazines for 10 mm are also harder to find than .45 and more expensive.

If you're serious about a bear gun, you don't want to go cheap/marginal/questionable on your component parts or quality of build.

For the money, get a Glock--relatively available, generally reliable and also pretty weather-proof and in Alaska you can have high-cap magazines.

Or, buy a Delta Elite or DW Bruin.   Or a S&W 610--one of the LGS has a 6" in stock (and they've got a Bruin too).  You'll probably want a shorter barrel but you can touch/feel and see if a revolver is for you.

Or build a .45 

Whatever you do, if you decide to sell your build make sure you get a rock-solid liability waiver signed by the new owner, even if s/he is a friend.

my .02, which might not be worth .02

I have both flavors.
The 10mm can be made to shoot very powerful ammunition. I would say it's similar to 357 magnum.
It would be appropriate for field carry.
The 45 auto can also shoot very powerful ammunition. You would need to handload it and tweak the pistol a little.
Either would be appropriate for field carry.

When it comes to real world practicality, the 45 auto is the hands down winner.  Why?
It boils down to availability of ammunition and the general knowledge base.
Generally, you can get 45acp ammo for practice fairly easily.
Such is not the case for 10mm.
Familiarity is the key to success in all endeavors,  and it will be difficult to get a supply of 10mm for practice unless you make your own.

To summarize:
If you don't load your own ammo, go 45
If you do reload ammo, go 10mm.

Here's a article Ammoland published about bear attacks ended by handguns.  It breaks it down by caliber when known.  Pretty interesting read.  The short version is that in 93 incidents 97% of the time a handgun was effective no matter the caliber. 
https://www.ammoland.com/2020/03/update-handgun-or-pistol-against-bear-attack-93-cases-97-effective/#axzz6IgDwtlwJ