What I do after doing a good job of cleaning, and as a final application, is wet down a patch with alcohol to help dry out the barrel and then wet a patch with WD-40 and scrub down the barrel really good. This is a great agent that will get rid of any last water or moisture in the barrel.

Anytime you put water in Steel or even Stainless Steel MLer Barrels it's gonna rust. Some may say that SS MLer Barrels wont Rust too but they do, it's a different kind of SS not the Food Grade SS that's much better at not Rusting.
Just make sure you go right to Patching and Oiling after the Soap and Water Clean.
As soon as I finish the Soap and Water Clean and Water Flush, I grab a different Brass Brush and spray Oil on it and down the Barrel, then give it a few strokes and then Patch it. Then I'll do the N013 Bore Cleaner patches untill it comes out clean, then Oil.
(BP)

I have gotten away from the flash rust I use to get. I use to use boiling hot water for the final rinse and then stand the barrel up to dry. Now I use hot tap water and start dry patching right away. Then as soon as the barrel is dry I use breakfree clp to oil it up inside and out. I do not get any rust on my patches like I did at one time.

While I have this thread going, I have another question I want to ask. What do you do if you are away from home on a hunting trip, and just don't have access to a spot that you can use hot water to clean the rifle. Suppose you do infact shoot it during hunting, what do you do for the next few days? Is there something else besides water to clean it with that night? Or what do you do?

you could clean the gun with patches and solvents just fine. I usually have my two burner coleman gas stove along to warm up some water.
Art

when i shoot away from home i field clean right after the shot using a windex/alcohol mix, dry patch,lightly oiled patch then dry patched again.this gets me a clean gun and gives the deer time to bleed out.if i'm using blackhorn 209 i use patches presoaked with hoppes...........karl

You could even use WD40 on some Patches, any kind of Oil. just some thing to Lubricate the bore while you brush it, then lightly Oil and Dry Patch and Im sure that'll get you by untill you get Home.
Now I dont know who Insist that you need (Boiling Water) I've never used Boiling Water....Hot Water is fine and so is just plain Ol Water with some Soap, Im sure you could get by without the Soap even if you had to. Heck you could just Spit on the Brush and clean it. Im sure the Brass Brush does most of the cleaning anyway.
If Im wrong Please quote....and I just use Pyro RS so dont hurt me too bad if you have to use a different Powder and need a different way to do it.
(BP)

Do what Dave recommends He has lots of guns and experience