Seems to be some interest here so I'll explain my procedure, which isn't too different from others already mentioned.
My go to rusting agent is Mark Lee's Slow Rust Blue #3 formula - just follow the instructions included with the bottle, it will work. After polishing the barrel down to 400 grit, degreasing the heck out of the barrel with whatever method you choose (I prefer Acetone), then apply the rusting agent. Do this with a cotton ball, soaked in the solution, squeeze out the excess, swipe each flat one time in one direction. The solution should go on in a sheen, not blotch up, if it does, there is still grease/oil present, degrease again. Lay down a second coat of rusting agent like the first, in the other direction along the barrel, swiping once down each flat. Then set the barrel out to "rust". In the winter here in the Ohio Valley, I use a cabinet that I control the heat and humidity in, set the barrel in there for about 90 min. In the summer around here, just hang it outside in the shade. Don't, let the barrel turn into a Chia-Pet, you are looking for a nice even coat of dullish brown rust. At that point, into the boiling water. I boil on a 3 burner propane camp stove in a steel container I welded up for that purpose - I use rain or pond water. Anything that gets your barrel into boiling submerged into boiling water will work however. Let it boil about 2 mins (Last coat, let it sit about 5 - 10 mins.). You gotta card off the black junk on the barrel after removing from the water and allowing it to cool. I card off the junk with a .025" soft wire 4" carding wheel (Brownells), mounted on a Jet wood lathe running at 300 rpm. Lightly card off the junk from each flat, then repeat the whole process. It may take 5 - 8 applications and 2 days to finish the job. I have never had to neutralize a rust blued barrel when I have completed. Lightly oil, and she should be good to go.
