Like many, I started out shooting a bolt-action 22 then moved on to bigger and better things. Although just tightening up the precision of one of those is one path to take, you might want to consider two others.
One is to go the Ruger 10/22 autoloader route, starting with the very adjustable 'match' stock (if they make those anymore), then upgrading the trigger block, receiver, and bolt to Volquartsen. Add a 1-inch Shilen match barrel and a custom scope mount to hold a top end scope, and there's not much out there that can come close to it. The best results I got on targets was with Lapua but CCI was next best, with higher muzzle velo. The only problem seems to be the bolt waxing up in very cold weather. It's a bit of a chore breaking it down to clean it, but that's life.
But it's still a 22LR cartridge with fundamental limitations. Alternately, move up to the small 6 PPC, or 6BR Norma cartridge and then you might be able to do at 300 meters what you could do with at 50 on a good day with the 22LR. Dialing in the correct hand loads gives you a few more adjustments to tweak too, besides just choosing which brick to buy. Just getting a middle-of-the-road consumer action then adding some serious aftermarket parts and some tweaking allows you to get some very impressive precision. Or you could just jump into the deep end, and set up something starting with Bat, Barnard or Borden etc., fitting it with a high-end stock, etc etc.
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That way, you can avoid chasing around configurations and parts that sort of, but not quite, get you to the results you want. It's also sometimes a tough call whether problems are because of the shooter or the equipment. If you start out with a solid high-end piece, the probability becomes very high that any problems are due to the way that you are using it. So you can concentrate on that instead of second-guessing your rifle or ammo.