I've used the exact same method as Stan for years, and it saves a lot of ammo and aggravation. It's more fun to use ammo shooting small clusters than walking holes around a target. I'd prefer to never use a collimator spud in the bore of any rifle that I was able to remove the bolt and see through the bore. I feel this way for the same reasons I'd avoid running a cleaning rod in the muzzle when cleaning from the breech end is possible. I just don't want to risk any unnecessary wear or damage to the crown and muzzle rifling. For my muzzleloaders, I have made nylon bore guides on the lathe to use when cleaning or shooting at the range. If I'm careful, I can typically bore sight to within a couple inches of the aiming point at 100 yards. Without even firing a shot, that's as close as a lot of guys seem to manage after burning up a whole box of ammunition. Two shots using the method Stan detailed will usually get the rifle dialed in, and the third shot erases any doubts.
Careful with old scopes, some need a shot or two to settle into the adjustment, so I wouldn’t necessarily adjust on every shot.
Agreed, except I have found that simply tapping on the reticle adjustment knobs with the end of a fired brass case after each adjustment seems to take care of any reticle movement lag, without firing extra shots. A couple light raps will do, and the brass is non-marring.