Sure you can kill a grizzly bear from 75 yards away with a rifle. Unfortunately you seem focused only on the actual shooting of the animal. The hunt is much more than the shooting.
Not to mention that when you shoot at a grizzly, you are picking a fight with an animal that is capable of killing you if something goes wrong.
Not to attack you or anything...
But we all know your a good shot, and being that you are using a .375 Ruger which packs more punch than a 375 H&H this part about the Bear fighting back is a little funny.
The Bear has NO chance at all...unless you miss....and if he is close enough not to allow a follow up shot.
Good Luck!
Hunting dangerous game can be as safe or as exciting as you wish to make it. Shooting a bear from 100 yards is relatively safe, provided your shot is well placed. All that interferes with that is a target that is inclined to move, fickle mountain winds, and adrenalin. But if that bear is wounded and gets into thick cover, you will have all the adventure you can handle. You know you are having an adventure when you wish you were somewhere else.
But stalking a bear, any bear, into thick cover to start with will ensure you earn your trophy. It doesn't matter what kind of rifle you carry, it will feel like a pea-shooter. Should hunting be done on horse back, a grizzly suddenly standing up in an alpine meadow could make quite the train wreck as well.