This is how I do it... it's easy, it's fast, and it's effective. Best of all you can do it while still on the firing-line and thus not offend your significant other with the usually pungent stench of commercial cleaners in your home.
Dilute regular household ammonia (sudsy is best but regular is OK too) to 2/1 or 3/1 with water (it can be as much as 10/1 if the smell really gets to you). Keep in a small bottle to take with you to the range but label it well so you don't mistake it for contact-lens solution or something (yeeeowww!)
After you are done firing and while still at the range moisten (not dripping-wet, but sorta-soaked) a patch and run it down the bore and back once. This instantly will neutralize and dissolve the corrosive salt-compounds from the primers and start in on the copper and powder fouling with a vengeance.
Let stand for thirty seconds or so (just enough time to take off and throw away the ammonia-patch you just used and put a new, dry patch on your rod). Run the dry patch (or several) down the bore and you are most literally done.
DON'T OVERDO IT! More ISN'T better in this case...
You really don't want to slop ammonia (especially if heavily concentrated) all over the blued parts of the gun (as it will likely start to remove bluing after 30 minutes or so) and you also shouldn't leave the ammonia in the bore for an extended period of time (like hours, although I do know folks who do that anyway) as that may (not WILL, but MAY) cause "crazing" (microscopic pitting) of the metal. I also have to caution against slopping ammonia on the wooden parts of your rifle, as it will usually strip the finish down to bare-wood, BUT if you follow my advise on HOW MUCH ammonia to use (only enough to dampen, but not soak, a single patch per gun) you will not EVER experience ANY problems at all...
If you are worried about primer residue getting on the bolt-face you may want to quickly wipe it with the wet patch before throwing the thing away and quickly dry it. Same thing with the gas-tube in a semi-automatic rifle... don't go overboard, just wet it and dry it and get done with it.
As a final precaution (since the ammonia will also kill all lubricants and leave the metal very dry) you can run a patch of gun-oil down the bore and leave it like that for protection from the elements (just be sure to run a dry patch down the bore before shooting it again).
I've been cleaning guns this way (including *every* gun we sell) for nearly thirty years, and have never had rust form in any bore (even here in humid Florida).
However, if you are (like some folks I have met) completely obsessed about leaving traces of ANY powder or copper residue in the bore of your weapon, you can certainly follow up your "field-cleaning" with a detailed, strenuous, traditional cleaning once you are home (or in a week or month from then). But I warn you... your bore is much more be likely to be damaged from your over-enthusiastic scrubbing to get out that "last speck of copper" (which has no affect on the actual accuracy of your firearm) than it will with all the rounds you could possibly send down it during your lifetime.
Years ago I was told by a gifted gunsmith that many people do more harm to their bores with extensive, and intensive, cleaning with the thought of getting every bit of powder, lead, copper, etc. out than by leaving a little in.
Though, I know people who will spend hours and countless patches until they get one that doesn't come out with residue on it. Them I pizz them off by running a slightly oiled patch through that picks up more. Then, they're back at it for a few more strenuous moments, lol.
Good point, I might add.
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"It confuses me how some people can vigorously go against the 2nd. Amendment and still call themselves patriotic"-me
