I have seen lapping done the way that Wilbur described, at a barrel maker's. I think that applying the compound that way might contribute to belling the muzzle. Of course that is not a problem for a barrel manufacturer, given that the gunsmith will cut that part off. Of course I could be all wet on this.
A friend has figured out a way to oil the bore, and apply the compound to the bore with a mop, after pulling the lap to the rear of the barrel. That way he can start at the back, and pretty much leave the muzzle alone. He has done this on a rimfire barrels, with good results, but be warned. He is as good, smart, and hard working as anyone could be, and one of the barrels took him 3 1/2 hours to do. Knowing him, he wasted none of that time.