Any copper that comes in contact with the sweets will be attached. The 'blue' is the copper compound generated by the ammonia's action against the copper, either in the jacket metal fouling or the implements used to handle the patch. Check where the blue is. If on the outside of the patch then one might assume jacket metal fouling. If on the inside of the patch, the jag is being eaten away. My experience tells me the jacket fouling is musch more suseptable and will be removed long before the jag is totaled. Plastic jags can be used but as a rule are pretty flimsy. I've never seen anything that I'd use in a bore other than brass. Never use stainless steel brushes as I believe the are much too aggresive. I prefer 1 piece stainless steel rods. As the most mobile of the cleaning system parts they are the least likely to embed any grit and wear the bores interior. I know, I know, the coated rods are not supposed to embed but stainless WON'T. When lapping a metal part the abrasive is embedded in a SOFTER material which is then rubbed against the harder material and the embedded abbrasive can attach the harder material, with the softer acting as a carrier. As an example see the diamond steels used to sharpen the very hard material used in a knife blade. The diamond material is embedded in nickle usually. A soft material used to hold the diamond to the core. A polished stainless rod is almost impossible to embed as the bore is softer than the rod!! The abrasive won't wear out my barrel. With proper technique and a stainless 1 piece rod I use a brass spear point jag and occasionally a brass bristle brush. Those with the brass wire have less chance of a wire end damaging the bore...they are most certainly not polished. As to patches I use whatever. The modern commercial patches are great but they are not appreciably better than something homemade. As long as it fits properly and is used with proper equipment it'll be just fine. When you've gotten to the point where there's little blue on the patch, clean a last time with a Hoppes time powder fouling cleaner and use the FoulOut. It will root out the last of the metal fouling and leave a really clean bore.. It should be rinsed with Hoppes and protected with a good oil. Either a light coat of ATF if the weapon is to be used in a short time, or a light grease such as RIG if it's to be stored long term.. Either should be removed before firing, with the oil being the easiest and the grease more difficult. Always clean from the breach if possible and always no matter what use a guide to avoid contact between the bore and the rod. One should use the heaviest rod(stiffest) possible to keep bowing to a minimum which will allow contact between the rod and the bore in the midpoint of the barrel.
Good luck and just keep after it. Jacket metal fouling(actually cupronickle fouling) can be a pain but leaving it in the bore invites pitting and a ruined barrel. Be aware also that as bores age they tend to roughness and this contributes to quicker jacket metal fouling. I've found the faast varmit calibers to have a poor track record. They can be badly damaged by simply not cleaning and getting them too hot. The rapid fire found in a dogtown for instance can lead to a burned up 22-250 pretty quickly. Only a clean bore and a scope will tell the tale.. Good luck from the gunnut69