When I have to clean with luke warm soapy water, After its been brushed and mopped out in the water bucket, I.....
#1 wipe the barrel down with a towel
#2 grab a can of Birchwood Casey Gun Scrubber " Or firearm cleaner" and spray the heck out of the bore. This product helps remove water and dries out the bore faster. Removes all MOISTURE.
#3 soak a patch with the above product and swab the bore
#4 dry patch
#5 light spray a patch down with Barricade
Put gun away until the next day when i have the urge to shoot it and clean it all over again.
#2 & #3 I feel is the best thing to do with any barrel when using water to clean fouling away. I do the same thing with my Mosin Nagant that shoots corrosive ammo.
Dont use that amateur bore butter - seasoning patches stuff, its all a gimmick to sell you something that SEALS IN any trapped moisture.