I think you'd have to waste a lot of ammo to pay for a bore sighter. I've never bothered with them. You can do a halfway decent job of bore sighting by just pulling the bolt out and looking through the bore with the rifle on sandbags.
However, I never even bother doing that. Just start with the target at something close like 25 yards or so. You have to be pretty far off to miss a decent size target backer at that range, never happened to me. Even if it is off, just move the target closer until you find out where the shots are going. If the target hits the muzzle and you still aren't getting holes in the paper, I'd suspect an ammo problem. ;)
Once you get it mostly centered at 25 yards, then move it out to your desired zero range and fine tune it.
I'd really try and correct the centering problem, if you don't you will either have to adjust your windage for different ranges, or just accept the fact that it will shoot 1"(or whatever) to the right.
Mike