I have been shooting a 338 lapua with 300gr matchking with great accuracy. What would be a good hunting bullet for long range brown bear?
A matchking would work at long range but with a close encounter I don't think it would cut it.
I use 270 grain Barnes XBTs or whatever they're now called--the new ones have cannula grooves. But you may want to try the 300 grains version. This year I loaded up some Barnes 350 grain solids and surprise--they shot to the same point of impact at 100 yards as the 270s. They are round nosed, but some form of copper bronze matrix, still not a real long range bullet, but then 500 yards isn't overly long range--for most game.
I'll not moralize here--just state my way. I wouldn't shoot any bear beyond, say, 200 yards unless there's snow on the ground and the bear really needed killing with any load/rifle. I killed a starving grizzly in a cabin on Thanksgiving day 2008. He was around 25 years old and his teeth were--and are--worn below the gums. He'd taken to visiting homes in an ever decreasing circle in our two adjoining villages looking for anything he could eat. The fore-mentioned was compounded by an injury he received in late August or early September; someone shot and hit him in his right rear ankle. Skinning later that ankle was the size of a football and gangrenous--so much so that anyone entering the shop got sick. The Discovery channel aired a report in their Alaska Most Extreme program April 16, 2009. A six-year-old girl daily sledded down the hill that led to the cabin I shot him in--every afternoon. I shot him a little after noon.
In many respects we were lucky; villagers were vigilant for over a month knowing an "ice bear" was in their midst. I hunted/tracked him for as long and been caught out after dark doing so--a stimulating experience. Dark means after 2PM here in late November; it's "light" around 11AM or so. Not much time. Nor would there be for anyone mauled and munched on by this wounded and desperate bear.
I think that for an over the counter bullet I would go with the Barnes 285 TSX BT, Barnes 250 TTSX, or the 225 TTSX. If you have the coin for custom bullets the GS line seem to be good. I dont think your gonna find any really high B.C dangerous game bullets. A few people have been reporting way better B.C's on the 285 grain Barnes than the published .585. which isnt that bead to begin with.