Great advice lilabner!
The best I have heard it described is that "breaking in" a bbl won't make your rifle shoot more accurate, it will make your rifle shoot accurate longer between cleanings. I have found this to be true. In the old days, I did nothing to break in a bbl, just cleaned it after a range session. Now, I clean with a method similar to lilabner's. However, I do clean after each of the first five shots.
The purpose is to prevent carbon tempering and to allow the rounds to lap the roughness out of the bbl. Actually, it is probably more important to break in the throat. The reamer marks left in the throat of a new rifle are across the lands. When a bullet is forced into the throat, at this temp. and psi, copper dust (from the bullet crossing the reamer marks) is vaporized and carried down the bore. As it cools, it is deposited in the bore. Subsequent bullets add deposits build up and make it difficult to remove later. So by cleaning after each shot initially, you're polishing the throat and not allowing copper to build up in the bore.
It has been my experience that my rifles that have been "broken in" will shoot tiny little groups longer than those that I didn't break in. Maybe just coincidence. I don't know? But my rifles that have been broken in don't start to open up groups until I have fed a lot of rounds through them, 50 or more. The rifles that I didn't break in tend to open up after a couple dozen rounds. Of course, the cal makes a huge difference in terms of fouling. This has just been my general impression.
Copper solvents will destroy your bronze brushes and give you a false indication of copper fouling. Use a nylon brush with copper solvents.
Of course, this is highly controversial, and I may be all wet. I rarely know what I'm talking about

But what the heck. Why not err on the side of caution? It really doesn't take that long to do, and once it is done - it's done. Take another rifle to the range with you. When you grow tired of breaking in the new rifle, grab the other one and start pokeing around with that. Besides, you're getting valuable info. while breaking in - zeroing scope, working up a load, checking for psi marks...