I also would recommend the .308. The venerable 30-06 is also not a bad choice but to get an appreciable difference you might have to get a rifle heavier and more cumbersome than she would be happy with.
Using a .308, she will have a very large variety of actions and models and will certainly find one that fits perfectly. That fit, along with the modest recoil will equal much more practice with said rifle and practice that will be enjoyable.
Many rifles, including the .308 will kill large Browns or Grizzlies at 300 yards, but I would bet that most guides would advise against shots that long at DANGEROUS animals, regardless of calibre. Good luck with your search!
If I can see it, I can hit it.....and I can see pretty well.
My wife shoots a 270 and a 308 likes them both, what we did
is cut open a gas vent system on the end of barrel but not a
muzzle break. Some what like setting a drill bit on the side
of the front and cut two vents on each side seem to work and
no great amount of noise.
The 308 Win will do all less big bear Northern Canada and Alaska.
Here's my take on the whole matter. Sure you can get away with a light recoiling .30 cal gun on dangerous game with proper shot placement. Heck, a whole bunch of elephants and cape buffalo have fallen to 30-06's. However, I sure wouldn't take one on a cape buffalo hunt, and I wouldn't take one on a grizz or moose hunt either. I'm a pretty experienced hunter and a fair field shot, and that experience tells me that sometimes even the best of us make errors that lead to less than perfect shot placement on big game animals. I've also seen alot of animals punched right through the boiler room run 2-400yds. Those things lead me to believe that I owe it to myself and the animal to use a firearm that is IDEALLY suited to the game and conditions I'm hunting in, not just barely enough to get by. And if that goes for me, it sure goes for the little misses too, especially if she's not as experienced or as good of a marksman as I am.
On that note I'd say no less than a 8mm/.338 on grizz and moose. If recoil is a problem, solve it with a good recoil pad and a brake, not by using a lesser cartridge. I haven't shot the .338 Fed or .325WSM yet but I've heard they are fairly tame in recoil for the ballistics they offer.
Browning A-bolt, the Micro or if money doesn't matter the Titanium Mountain rifle in 308 Win. It is a very proven round and can get over 200gr bullets for close dangerous game if you handload. Also I sold my 338 WM once I got my 300WM set up because for the same weight bullets, the 308cal has a better BC. The 308win would be great for Varmint with 110gr HP's and great for 200yard or less Brown Bears with the 220gr...I think there is a Partition or any of the Barnes bullets.
I like the A-bolts alot, nice detatchable mag, good bolt throw and the Micro's are pretty light to boot, put a user friendly ( ask around to get opinions on the most user friendly, noise wise) and it would be a great rifle.
I am waiting to buy a Micro in 7-08, but I don't have the desire to kill big bears, just Elk under 500yards.
Well it's no surprise that the smaller diameter bullet at the same mass will have a better BC, that's just a function of a higher sectional density. A 7mm will have better BC at the same wieght as the .308, that doesn't mean a 7mm Rem Mag is a better dangerous game cartridge than a .300 WinMag Apples to oranges.