I should make a business out of sighting in other peoples firearms, I would become a millionaire in mere weeks.
When I buy new scopes for my rifles I sight them in with 4 shots, and we're talking about .5 MOA groups in the bullseye at 100yds after.
Seriously, all you gotta do is shoot the rifle at 50yds, the sight cannot be so off you cant hit at 50 so you will make a hit. Then you guess the distance to the bullseye in elevation and windage. Look at your scope adjustments, if its 1/4 MOA each click will change the point of impact by .25 MOA at 100. At 50 you need twice as many clicks.
So I shoot at 50, hit, make the adjustments, the next hit should be very close to the bullseye, then I go to 100, make a shot which is usually off by 1-2'' in elevation, make a final adjustment and the rifle is sighted in dead center.
Then I shoot a 5 round group just to verify zero. Done.
If you need more rounds than that the barrel might heat up which, when burning hot, will change the point of impact and thus zero will shift around making you crazy.
After you sighted in the scope/dot don't touch it, don't bump it, don't tighten or loosen its screws, and remember the scope is sighted in for one brand of ammo, changing the brand and bullet weights will change the point of impact. Also when dis- and reassembling the gun use a torque wrench to make sure the action screws have the same tightness.
Also one common mistake people make when sighting in guns is using an awful rest, most of the time a front rest but no butt stock rest. Which leads inexperienced shooters to shoot shotgun-like patterns at 100 and that way you cannot even guess the current point of impact so trying to sight that thing in becomes a fruitless and expensive endeavor.