I've shot a lot of pigs with the Nosler 55 grain Ballistic Tip, and it works fine, though I keep worrying that it might be a bit too explosive and not penetrate as well as I'd like. In my 223 I've switched to the 65 grain Sierra Gameking, and it does seem a bit less explosive (but it is moving slower). It should stabilize in your 22-250, and I base that statement on knowing that the 63 gr Sierra flatbase stabilizes in my 220 Swift with the 1 in 14 twist, and the 65 gr Gameking supposedly has the same bearing surface. Bottom line...if you're shooting little pigs, the 55 grain will do fine. If you're gonna shoot seriously big pigs, the heavier bullet might be a good choice. Better yet, the 60 gr Nosler Partition really penetrates, though I don't have a gun that will shoot it into tight groups. Still, I shot a Partition through a medium sized pig the other day, and I shot it the long way through, starting at the rear.
As for the rear bag, I use one on the bench, but you might be able to just use your left hand to make a fist around the sling and swivel at the rear of the rifle. That works pretty good to stabilize the butt of the rifle.