36 yards, 100, 300, etc?

Bore sighting is not a science. It is a WAG using fairly unreliable tools relative to the sighting system mounted/used on your weapon.  These are either a collminator type bore site (usually not usable on AR type due to height of sights over the bore) or laser based units, which (IMHO) do poorly on elevation issues for too many reasons to elaborate here.  

Bore sighting is NOT a substitute for actual range time with real ammo!

Any firearm that is bore sighted MUST be fired at the shortest possible range (25yds or less, if possible) to make sure it is on paper (the target) and adjustments made. Some ranges (like the one I use) have a min range of 50yds, which can present problems.  Some ranges, for shooters not known to the Range Master/Range Officer, require the shooter to shoot at their shortest range so that zero can be determined before they are allowed to shoot at the longer ranges.  

UNDER NO CIRCUMSTANCES SHOULD ANY FIREARM ASSUMED TO BE "SIGHTED IN" BY BORE SIGHTING ONLY! Yes, I am shouting!

ETA: BTW, to answer your question, Bore sighting is not related to a "range/distance"

+1 on "shorter is better." Last weekend I put a new LaRue/Eotech combo on my AR and took it to the range. Eotech literature states it is pretty well dialed in (not a direct quote, but my impression of their statement).

So I put a couple of Shoot and Sees on a 42" diameter cardboard circle and tack it up @ 100 yards. Shoot- nothing. Shoot. No hole anywhere. I was the only one at the range, so I strolled down and had a closer look. Couldn't see any evidence on the ground, which was smooth after some steady rain we have had. Must be high, I deduce.

Drop back to 25 yard target. No hole. Shitski. So I shoot at the bottom of the target and find I'm shooting 2 feet HIGH. Fortunately the berm behind the 100 yard target is super highand the pistol range on the other side was vacant as well. I don't know what my Eotech was originally dialed in for. About 600 yards, maybe.

Quoted: +1 on "shorter is better." Last weekend I put a new LaRue/Eotech combo on my AR and took it to the range. Eotech literature states it is pretty well dialed in (not a direct quote, but my impression of their statement). So I put a couple of Shoot and Sees on a 42" diameter cardboard circle and tack it up @ 100 yards. Shoot- nothing. Shoot. No hole anywhere. I was the only one at the range, so I strolled down and had a closer look. Couldn't see any evidence on the ground, which was smooth after some steady rain we have had. Must be high, I deduce. Drop back to 25 yard target. No hole. Shitski. So I shoot at the bottom of the target and find I'm shooting 2 feet HIGH. Fortunately the berm behind the 100 yard target is super highand the pistol range on the other side was vacant as well. I don't know what my Eotech was originally dialed in for. About 600 yards, maybe.

Same with my Eotech.    Since I got it sighted in its been fine but the first time was such a surprise.  I started at 25 and could not believe I didn't hit paper.  Eotech does imply that the sight should be close to zeroed when mounted.  Glad I started at 25 and not 100.