"You can't use 40 short and weak ammo in a 10mm"
This isn't true. Most 10mm handguns will function just fine running .40S&W. The case is the same except the 10mm is 3mm shorter. Also, most modern commercial 10mm ammo is downloaded to near factory .40S&W velocities. I don't know why you would carry a .40 for bear protection but for either the 10mm or the .40 in bear country you would want specialized deep penetration ammunition from someplace like Buffalo Bore or Underwood. Ammunition designed for defense against humans does not generally work well against heavy game as they often do not penetrate deep enough to reach vital organs and will fragment when they hit bone.

Here is an interesting read on handguns used in actual defensive encounters with bears.
https://www.ammoland.com/2024/05/bear-defense-with-handguns-update-20-more-cases-98-effective/
Go through the original and all the update links.

In many cases people stated that from the time they were aware of the bear to the bear being on them was around 2 seconds. Consider the type of holster and where you carry it as well. Most people cannot draw as quickly from a chest rig vs a holster on the hip.

My vote for a survival/bear gun would be a Remington 870 with a 14" barrel and ghost ring night sights. Add a sling and a receiver mounted ammo carrier. Carry different loads for different jobs. Birdshot for grouse/quail, maybe some buckshot and Brenneke Black Magic Magnum for bears. https://www.brennekeusa.com/brands/hunting-ammunition/black-magic-magnum

YMMV

topgun260 wrote:"You can't use 40 short and weak ammo in a 10mm"
This isn't true. Most 10mm handguns will function just fine running .40S&W. The case is the same except the 10mm is 3mm shorter. ...

I was curious about this since they both headspace on the case mouth.
From what I read, if the 40 will cycle in a 10mm pistol, it might work,
IF the extractor holds the case in the proper position.
If the extractor doesn't hold it, the cartridge will go farther forward until the case mouth bottoms out in the chamber--
then maybe the firing pin will still strike the primer (or maybe not).
Then maybe the empty case will eject, making follow-up shots possible (or maybe not).
Don't think I'd wanna bet my life on those maybes.

First of all, I wouldn't recommend using .40S&W ammo in a 10mm handgun for bear defense. If you have the 10mm handgun, use heavy game 10mm ammo in it designed for hunting or bear defense.

As for shooting .40 through a 10mm, yes, lots of people do it especially for practice as your budget .40 ammo is generally cheaper than 10mm.
I have personally shot hundreds of rounds of .40 through 10mm handguns with high reliability. There is plenty of info about this online if you search but in personal experience the Glock G20 and G40(long barrel 10mm) function fine using .40S&W. The Sig X-Ten runs fine on .40 too.

As always YMMV