I think there are lots of facts that could be involved as well. My recommendation would be that if you are going to stick with your factory setup/stock, then I would break it all the way down (remove scope and pull the action out of the stock). The Ruger Americans have a good bedding system, but the stocks aren't the best. I would get a broom stick and wrap it some heavy grit sandpaper and take about 1/4 inch out of the front of the stock tip. Then reassemble action into the stock, put your bipod on and get down and load the bipod as you would in the field. Have someone take a thin piece of cardboard or thick stock paper (credit card or better thickness) and have them try to slide it all the way down the barrel to the action. If it's free floated when the bipod is loaded, you should be good. Torque the action back down to the proper specs and in the proper order (front or back first) based on Rugers recommendations.
Now on to the scope. Order a scope level kit from Midway/Brownells or one of the other online shops. The Wheeler one with two levels is pretty good and only like $35. Good piece of kit to have for future rifle builds or if you upgrade you optic down the line. It will always be useful to a shooter, get one. Make sure you base is torqued proper to the action. Get your level on there then the barrel level matching. Now put on your ring bottoms and torque to spec (I always lap rings too, but that's just me). Now get your scope installed and level the top turret to the barrel level. Lock the tops down and re-verify level. Reticals always look canted to me when shouldering a rifle, but I know they aren't. On a pod they always look good. Now you should have a solid platform.
Now run your box test on your optic. You can do this in your backyard without ammo if you can solidly mount your gun in a vice. Just put some dots on a board in a box at equi-distances. Keep count and dial in/out till you hit all points. Then try repeating using the counts you came up with the first time around. Things should hit the same places again.
Next is ammo. Not sure how factory precision ammo is for the 06, but lots have them so would figure should be plenty. You will have to try maybe 5-10 different boxes if you aren't reloading till you find one your rifle really likes.
Finally will be trigger control and form, which have a HUGE impact on repeatable/consistent shot placement.
Also keep in mind that thin barrel will heat up and throw shots after your second or third one, so you should wait about 10 mins between 3 shot groups till your barrel fully cools. Maybe switch out that 06 for a Ruger American Predator in 6.5 Creed if can swing it. They are known to shoot, even from the factory stock surprisingly.
Good luck!
