With my Henry, .44-40, Goex 3f, Lee 2 groove bullet, 50/50 Crisco/beeswax lube:
-wipe it off and take it home. Have a beer, go to bed. Got to work the next day. After work, get the Henry out to be cleaned.
Letting it set overnight lets the fouling absorb just enough moisture to be nice and soft. With a well shot in rifle you can wait several days if you want. Just me, but I don't like the case in the chamber method. I want the chamber to get the same treatment as the rest of the barrel.
-With the rifle upside down over the sink, action open but elevator still down, soak a patch in tap water and run thru the bore. Flip the patch and run it thru again. Repeat with a dry patch. Repeat with a patch soaked in Ballistol.
(The patch does not need to come out white . That would be removing the nice oily grease. Yer not trying to remove copper fouling here)
-Soak a few q-tips with Ballistol and work around the elevator. Dribble a few drops into the action here and there. Dribble a few drops into the magazine slot and work the follower up and down a few times to spread it around. Wipe the whole thing down again with an old greasy rag and put away.
-Every couple of years or so, take it apart and inspect. No rust yet after nearly 15 years. Do the revolvers much the same. Shotgun is a hose down the barrels, paper towel wads, and a shot of spray Ballistol.