The greatest benefit to carrying a gun in wild places is that it gives you the confidence, though not the wisdom, to make good decisions. Whether or not that confidence is false, is up to you. Learn as much as you can about bear behavior, reading the trilogy of bear attack books by James Gary Shelton, and Stephen Herrero's book are a good place to start. Learn bear anatomy so that you can find the benchmarks for making a stopping shot rather than a killing shot, protection isn't hunting, and you should avoid shooting center of mass. Make sure your wife is capable with the rifle and if you can afford two, she should have her own. My wife's rifle is a lightly customized Husqvarna 1640 Carbine in .30/06, cut down to fit her, it has a Ruger barrel band front sight with a rectangular post and an XS ghost ring rear sight. A .30/06 is an intelligent minimum for a protection rifle, even in polar bear and grizzly country, and the .308 is only a short step behind it. If you're hiking in the bush with that rifle slung across your back, it is not available to you; if you need it, you'll need it quickly. Work out a convenient carry method that doesn't result in undue fatigue and that enables you to get the rifle into action quickly. If you are in the habit of carrying a pack, don't take it off when you shoot, the sudden change of weight will thrown you off balance when you need to make a snap shot. Practice should be frequent, but the duration of the practice need not be long. Set up your targets about 5 yards away, shoot as quickly as you can, either after picking the rifle up, or after first having to unsling. When you fire, cycle the action hard and fast and fire a second round as quickly as possible. Your two shots should group no larger than a cell phone, and the first shot should sound no more than 2 seconds from the time the rifle butt hits your shoulder. You will benefit from dry fire drills before going afield.
A semi-auto rifle makes a lot of sense since it will reliably cycle every time, where a manually actuated action can be short stroked under stress, bud I don't believe the requirement for an 18.5" barrel, or 5 shot magazine should be a show stopper. That said, I think you could do very well with a Remington 760/76 pump rifle. It is available in a carbine configuration, it's thin profile makes it pleasing to carry. The detachable magazines can be either a blessing or a disaster; a blessing if you have several, since spare rounds can be conveniently carried in a packet, making recharging the rifle very fast, if that is something that matters to you. DBMs can be a disaster if the one magazine you have is lost, forgotten, or misplaced. Although far from common, these rifles were chambered in .35 Whelen, but the commonly available .30/06, loaded with 180 gr bullets will do all that needs be done, with energy to spare.
I grew up with bolt guns, and those will always be my preference. I've tried to warm up to lever guns, they bruise the knuckles of my shooting hand unless I warp my fingers around the outside of the lever, which works after a fashion, but leaves much to be desired. The Remington M-7 is a nice compact package, and I believe its still available in .350 Magnum, although in such a short light rifle, that might prove a bit much for your wife to manage, so the .308 version is likely a better choice, if you will share a single rifle.
In a protection rifle, I'd send every Remington to a gunsmith to have a barrel band, rectangular post, front sight installed, install a ghost ring rear sight, and have a large handle bolt installed, and to ensure the factory bolt handle won't peel off if under hard use, particularly if you experience a sticky round. If the rifle is not wearing a scope, a notch can be milled in the receiver for stripper clip loading, which is even faster than magazine changes. Something I like to do is move the front sling swivel stud from the underside of the forend to the radius of the forend tip. In this location it can't cut the hand when the rifle recoils. I ran into yet another example of a Remington bolt failure just a couple of weeks ago, this one in a .270 chambered 700 Remington. The neck sized only round was difficult to chamber and he broke off the bolt handle when he attempted to force the bolt handle down, so then he had a loaded round in the chamber, and couldn't fire the rifle since the bolt was out of battery, but he couldn't eject the loaded round either. I was able to get the bolt open, but didn't have an cleaning rod with me to tap out the stuck round, so that was on him.
A Ruger Gunsight Scout in .308 might be more to your liking, since 10 round magazines are available, and it comes with good factory ghost ring and post sights already installed. Another little rifle that has my attention is the Howa Alpine, another short action .308 carbine, although factory iron sights aren't part of the factory package. If you choose to scope your protection rifle, it should be with a low fixed power or a low power variable with a wide field of view, and a reticle that is easily picked out against a dark background; problems frequently occur at night, or in subdued light.
