I suspect very few factory rifles will shoot actual .5 inch groups with factory ammo. Actually, just over an inch, say 1 1/4", is a good level of accuracy for BG hunting. If you are looking very long range, say over 350-400, it is best to start with a more accurate gun, something under .75 moa, or better yet .5 moa ish.
Couple other thoughts. Did your rifle shoot better in the factory stock? Is your B&C stock pillar bedded or one with the alum. bedding block? If not, I might glass/pillar bed the action and make sure the barrel is free floated. Bedding can make a big difference. There are custom ammo companies that will load a box of ammo, where there are 4 different bullets, to see of your rifle likes one. Superior Ammo comes to mind.
Lots of quality guns, where 1" groups or better are regular. Savage, Tikka, Howa/Weatherby Vanguard, Remimgton, etc. The Ruger American is accurate and usually under $500, their Hawkeye is under 1k and shoot well.