If I've had to do a serious deep-cleaning down to bare metal plus soak everything I can out of the pores, then I typically smear a dab of whatever bullet lubricant I will be using on a clean patch and jog it through the bore a few times end to end, followed by one clean patch straight through as an attempt to prevent new leading on the first shot.
I only clean my benchrest match rifles once a year, at the end of the season. I do what Ian does: a soaked patch of my match lube (Grey #24) and rub it well into the bore. One dry patch at the beginning of the season, and I'm read to shoot some foulers. At the end of the each day, one damp patch of Ed's red. Next day to shoot, one dry patch and shoot foulers. This only when I go East where it is damp, like Iowa or Ohio. Plinkers get wiped off and a dry patch at the end of the day. Did I tell you there is an advantage to living where the humidity is 10%?
Same here on leaving the bbl alone if the load is not leading, and this is extremely rare for me
now that I have learned how to do it correctly. Clean the cylingers of revolvers, the chambers of
semiautos (although pretty rarely) and good to go with a good lube and a good load.
I shoot a LOT of new and very low round count factory rifle barrels. They start out getting reasonably "deep" cleaned with Remington 10X and grey JB in their early lives. They don't get lubed to start the next string. Somewhere around 100-150 rounds they "should" be coming into their own.... where dry mopping every 20-40 rounds keeps the bore shiny and happy. The only reason I use any barrel lube or oil is if it's going in for long term storage.
For the most part these are varmint rigs,NOT target guns. 1st round X's count,irrespective of pretty much everything...... I can get 3 shot groups that cloverleaf "usually" within the development period. 5 shot,pretty durn tight groups out of about half of the rigs..... in,traditionally accurate jacketed chamberings. 222,6mm,'06....
It was very windy yesterday,so carried my R700 CDL '06(avatar rig) loaded with 175's. I had forgotten how heavy a nice piece of walnut is. I have gravitated towards light weight for so long. If I was competing in formal BR..... would spend way more time on stock design and bedding. Along with a different approach to a seasoned/fouled bores. Best of luck with your project.
If I do a down to the bare metal type pf cleaning I end it with an oiled patch. In a "rough looking but possible to shoot cast in maybe" mil-surp i have done the bare metal thing and then run a patch with bullet lube on it down the bore to pre-season. I don't know if it helps but I don't think it hurts. It's going to take 15-20 rounds before things start settling down anyway. And like many others, I very rarely clean a barrel hard. Wipe the outside down, maybe lube a bolt, but a good shooting barrel gets left alone unless it's been real wet.