Assuming the barrel is sound to start with, you should do much better than that. The condition of the muzzle is very important and a re-crowning might be in order if the muzzle is worn, gouged, or puckered. The condition of the throat and degree of barrel erosion is important too, altho I have one which gauges .307 on the GI gauge (just about at the reject limit) and it still prints 4 in groups.
Bedding should be checked as well. First thing to look for is that the recoil lug fits tightly and squarely on the lug seat in the stock. The lug seat can be shimmed with brass or pop can shims as necessary. Next check to see if the barrel is rubbing anywhere in the stock,except for the forend tip,and relieve this area. The barrel should rest centrally in the bottom of the forend tip with about 5 lbs pressure required to lift it out of contact. Some rifles shoot just fine with the barrel floating free of contact here, but you need to check to see if the barrel is in contact with the upper band which is ruinous to accuracy. If you find upper band contact you can shim around the seat for the receiver tang above the rear guard screw to tilt the rifle down in the bedding(kind of pivotting on the receiver lug seat).
The guard screws must also be tight. Turn the front one down "gorilla tight". Make sure the metal bushing which surrounds the rear guard screw is in place as well. One last point on the bedding; the rear tang of the receiver must not be in contact with the stock otherwise it will tend to act as an unintended recoil lug and work against the tight fit of the recoil lug on the stock seat. This condition will inevitably lead to the stock splitting behind the tang. You see this on many stocks.