Ok , more specifically , I was shooting off a Caldwell lead sled without any wind ( range was very protected). I'm shooting Hornady 50 grain Varmint SuperPerformance Vmax.
The scope is a Bushnell 4.5 x 12 Trophy XLT.
The groups at 100 yards would be within a 50 cent coin, but at 200 yards they are out to around a 3-4 inch circle. I can't say whether they were tracking or not. I didn't know to look for that. I'm very much learning at this stage.
I would start out with a few more trips to the range to familiarize yourself with the particular rifle.
If your 100yd groups are nice consistent round groups then I probably wouldn't say that it's "stringing" the groups and there might not be anything wrong with the bedding at all.
I did separate the stock from the action because I was having a problem with the bolt release lever not returning to the rest position. Once I pushed the lever and removed the bolt, the bolt would just continue to slide off the action without any stop. I probably disturbed the way the action was nested in the stock for 50 years. It did seem to hold a better group before I took things apart. I didn't torque the action screws to any specific number. I was just snugging them up for fear of causing some bending of the action. From what I've been reading that was probably not good!
It is possible that R&Ring the action from the stock placed the barrel into a different placwe and made for a odd pressure spot on the barrel.
Pillar or glass bedding the action will help with more consistent placement...but I wouldn't jump into big mods on the rifle right away.
Unless I find an obvious big problem, I like to put at least 50-100 rounds through a rifle before I pass judgement on making a major modification.
Try loosening the action bolts so they're barely snug hold the rifle butt-down and bump it off the floor a couple times. Hold it by the stock, not the barreled action otherwise you might pull it back out of place again.
This will seat the action back against the recoil lug and probably center it into any "dimples" in the wood where it has been sitting for probably quite a few years. Tighten the action screws. Do the front one first and the back second. 15-20in/lb is a good torque figure for a plain wood stock with no bedding block. That's not much...roughly 1/8th of a turn once they're snugged down. The sequence is more important than the torque spec, although both play a part in getting the action back into a consistent spot in the stock.
Give it another trip to the range and see if it groups any differently.
What kind of groups can I expect to get at 200 yards with off the shelf varmint loads like I previously specified? I don't reload (yet) but may get into it because I really enjoyed my first summer of retirement . Am I asking too much to get the group down to within an inch group at 200 yards? Should I just try different loads first? Should I take things in steps like add pillars, then bedding then partial relief of the barrel?
I did clean the hell out of the barrel with Remington Bore Brite and a brass brush. I don't think the gun was heavily shot? My Dad only used it for chuck hunting and with 6 kids didn't get out much.
Each rifle is different, but if you're getting 1" groups (50-cent piece is close) at 100yds, then you should be able to do 2" at 200yds. That is what is commonly accepted for factory ammo out of a bone-stock rifle. Some might do better, or some might do worse. Way too many variables to say that it's set in stone though.
Keep in mind that as range increases you're also introducing more possibility for shooter error too...the crosshairs cover twice as much target area as you double the range so there's a bit more chance for error. A twitch or breath that will "pull" a shot 1/8" at 100yds will magnify to 1/4" at 200yds. Etc...
The .222 is generally a very accurate little cartridge regardless of what rifle its shot out of, so it is possible that you might be able to do better.
I would try a couple of different factory loads first. It is possible that your rifle just doesn't like the 50gr Vmax load. My experience with the Hornady factory ammo is that it's pretty darn good but it doesn't hurt to try another brand or bullet weight either.
Depending on what's available in your area, I would try the Winchester 50gr SP load first, and maybe the Hornady 40gr Vmax load. If your local shops carry Fiocchi ammo, they also have a bunch of loads using the Hornady Vmax bullets. cheaper than Hornady ammo but they've still been pretty consistent from my experience with it.
I've got a friend with a beat up old 340 Savage in 222 and it just dearly loves the plain ole cheap Sellior&Bellot 50gr SP load...as in one-hole 5-shot groups at 100yds.
Keep us posted with what you find.