The procedure I use for bore sighting a handi is as follows:
I always start out with the scope reticle mechanically centered by placing a mirror against the objective lense and looking through the scope, you will see 2 pairs of reticles, one is the actual reticle and the other is the reflection of the reticle in the mirror. Move the turret adjustments so the two pair are lined up and you see only one reticle set. On some scopes this doesn't work, but on most will work fine. Experimenting with light source angles or a different mirror will usually work.
1. open action and place in a stable rest, the lohman works great for that.
2. I shine a laser pointer thru the bore so the beam shows up on the wall at the end of the hallway ~20 yds away. A spot/target on the wall would work as well to be seen thru the bore.
3. I use a trisquare level placed against the side of the action to make sure the rifle/scope is aligned perfectly in the up and down position.
4. I have a plumb bob hung at the end of the hallway, the string is used to align the vertical x-hair. If it's not perfect, I loosen the scope rings and adjust accordingly.
5. readjust the rifle so the "target" or laser beam is centered in the bore, then adjust the scope reticle to intersect with the laser beam.
6. If the turret has to been adjusted many clicks to align the reticle with the target, I know there is a scope mounting/barrel alignment issue and needs to be dealt with either a mount/ring position change or shimming or with the Burris Signature offset insert kit which I have had to use a few times.
Using this method, I very rarely need to shoot at 25 yds and start at 50, I've even been so close at 50yds that I move immediately to 100yds after only one shot and make my final sight in there. When I sighted my 357maxi in, I never even adjusted the scope, it was shooting 1½" to the right at 9 O'clock, dead center at 100yds. at 50yrds is was cutting the edge of a black 1" bull.