It depends what equipment you have. A lathe makes it easy. Drive a slug through the bore so that you are sure that it fills the grooves. Centre up a piece of scrap and drill an undersized hole, which you then carefully enlarge with a boring bar until the slug will just enter it. measure the hole and you have your groove diameter. Turn down the outside of your piece of scrap until it is thin enough for you to hacksaw through one side of it longitudinally. This is now a split sleeve with which you can hold the slug in the lathe chuck. Turn of the lands of the slug until smooth, then measure it. This is your bore diameter.
Fred

Really good tips, thanks to both of you; if a guy had a lathe, and had it set up. and knew how to use it.   
  I've got one, but fail so far on points 2 & 3 .  just not had time to rewire the basement for workshop yet-----or time to learn how to use it.

have a set of 4 Brown & SHarpe expandable ball gauges up to about .50 that do well measuring bores  as long as they are not rodded out  they'll reach about 2 "  into the muzzle end and are small enough to drop into most chambers to get the other end

I've done a low tech (cheap) bore and groove measure that seems to work for odd number grooves, but may not be accurate enough for some folks.

I got a regular push pin for a note board and flattened the point. Glued the handle of the pin to the spindle of a mic. I forget, but used just a spot of glue that came off easy later with just some solvent. Then zero the mic or take a reading for what zero would be.

Anyway, a bore slug, or maybe cerrosafe of just the bore part should sit on the anvil at the groove depth. If needed, I don't think so, a v block or half circle can be rigged up for the anvil side to steady the slug. Then, rotate the slug and take readings, with the small flat on the pin, down on the lands and up on the grooves. Subtract double that difference should give the bore measurement.

It's been a while since I did it that way, hope it makes sense or even helps a bit. Just one way to get a reading down in some tight spot. Probably could rig up something similar on a caliper. I can't remember where I picked up the idea, but I'd give credit if I could. Might be an option for some folks.

Oh, god my head is hurting,   a mathematical formula,  HELP.

I have a friend who owns a large engineering business and wanted to be able to do this. I worked out the maths, as shown above and pointed out to him that the vee block angle is unique to each number of grooves. His tool room manager told him that to make a set of vee blocks with sufficient accuracy would cost rather a lot and he gave up.
Fred

For the original post, I would slug the barrel and then use regular mikes to get the land diameter, and the groove diameters. Easy if it is a even number of grooves, and not to hard if odd, because with the lands of the bullet being so narrow, you should be able to get pretty close using calipers or just make a shim for the depth, the same as in the first post I did for checking it. I would think that using cast bullets just using calipers would be fine.