I believe a lot of the barrel break-in routines were for cut-rifled barrels, where a lot of wire edges in the bore needed to be burnished. Butta9999's routine is typical of many, but I've never understood the logic behind gradually extending the number of shots between cleanings. If the idea is the cleaning will remove metal fouling to keep the steel exposed to burnishing by the next shot, then surely you want to clean after each shot until the burnishing is completed, then shoot normally.
Today, if you have a hammer-forged barrel, the bore is already work-burnished. Only the toolmarks in the throat will need any burnishing. That can usually be done by cleaning between each round for twenty rounds. Use Boretech Eliminator or some other good copper and powder dissolving chemistry. Using JB or Iosso Bore Cleaner or the Remington cleaner may speed that process a little by polishing the throat slightly. I won't hurt and doesn't remove enough metal to widen a bore even a tenth of a thousandths even using it for every cleaning the gun ever gets. A stubborn throat with really bad toolmarks may justify light firelapping with 600 grit or finer abrasive embedded in cast bullets, but save that for a really stubborn case. If you aren't familiar with the process, read up on it.