Bore is fine.
Everyone knows what you are talking about.
But as 243winxb said, technically, the actual bore, as drilled through the barrel, is measured to the tops of the lands, while the grooves are deeper.
Using a 30-06 rifle for instance, the "bore" made by the drill bit is .300", or .30 cal, while the groves made by the rifling cutter in the bore hole are .004" deep x 2, or .308" across.
SO, it uses .308" bullets, not .300" "bore size" bullets.
rc