I agree with the others: .30-06/.308, and the selection you made, Ruger 77 in .30-06 will give you not only a good bear rifle, but a versatile rifle for virtually any other game this side of Kodiak Island.
I have hunted the Trinity Alps for deer, so can say that you could easily end up with a close... or long shot. Just depends. There is some really rugged country up there.
I killed a 250 pound black bear in Shasta County, just north of the Eel River, a number of years ago, with my .280 Remington, 160 gr. Nosler Partition handload. One shot. About 100/110 yards.
Read all you can about stalking bear. Without dogs or baits, it ain't nearly so easy... unless you get lucky. Hope you have a partner with you.
Best of luck, and good hunting. J.B.
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