do you measure the bore with a caliper?
No. You "slug" the bore. That is, to take a bullet (swaged, or pure lead - needs to be as soft as possible) and gently force it through the bore (usually tapped in with a wooden dowel and rubber mallet; and the barrel is thoroughly lubricated). The slug is then measured with a V-anvil micrometer (expensive) - calipers aren't accurate enough; and a conventional micrometer may not capture the true diameter.