Orienting-truing telescopic sight?

[Naphtali]

I've just completed parts acquisition for my Ruger 10/22 small game rifle. And I've run into an ignorance problem. This is my first firearm on which I use a telescopic sight.

Telescopic sight mount is Weigand's Integramount. Scope alignment with rings becomes a non-issue. That's good.

Scope is a Nikon Buckmaster 4x40, the largest objective lens scope with one-inch barrel the mount accepts. That's good.
***
I have no special tools to accomplish the following.

1. While scope can be aligned perfectly with mount's rings, this may not assure mount aligns with axis of bore. How do I do this?

2. Having successfully aligned mounted scope with axis of bore, how do I true/square crosshair sight picture with rifle squared to target? What I mean is if I rotate scope barrel axially to superimpose crosshairs on a rectangular bullseye, this does not address whether the rifle is square before I rotate the scope. If I don't rotate from a squared rifle, I'll have no idea what I'm rotating to. I could clamp the rifle to a rifle rest on a shooting bench. Or I could clamp the rifle to a rifle cleaning fixture on a shooting bench. But why should I assume the bench is square to anything, or any fixture will automatically align a rifle squarely to fixture's base?

I'm getting a headache. Am I worrying about nuances that don't matter?

[Lead Fred]

1) start at 10 feet away, adjust your group into one inch or less, then move to 25 feet. At 25 feet you should have your windage (left and right) down. Then all you have to do is adjust elevation for how far out you want.

2) I use a round bubble level (you can get them at RV shops). vise your rifle. level the reciever, then set the level atop the elevation knob cover. Rotate the scope in the rings until the bubble is square.

then its party time [smilie=p:

[Pepe Ray]

IMHO, YES!
You're trying to fix trouble without finding any.
set the rifle in a cleaning cradle. Eyeball it square.
Mount the base(s) and rings. Eyeball it square.
Install scope (do not tighten) and Eyeball it square.
Shoulder rifle. pear thru scope to move to optimum eye relief.
Recheck square. Replace in cradle and tighten rings.
Enjoy.
Pepe Ray

[jsizemore]

I mount a bipod to the rifle and rest the butt in a rear bag. I lay a spirit level (carpenters bubble level) just in front of the bipod to correct the level of the table. I hang a red chalk line at 100 yards and look through the scope at the chalk line. Rotate the scope and tighten the rings when the vertical crosshair is in alignment with the chalk line. Shoot gun and adjust mount and/or scope to achieve shot and center of crosshair alignment. Make gross adjustments with mount and fine adjustments with scope.