If there were a way to copper coat bullets at home, the equipment would be very prohibitively priced. Especially with the price of copper lately. If you insist on copper coated bullets, you're better off buying the ones already made that way. Personally, I find it easier to clean lead residue from a barrel than copper fouling. Hoppe's No. 9 solvent will dissolve lead, but not copper.
The first time I shot lead bullets in my Taurus 85 38 special it leaded badly on me. I was using someone else's cast bullets which were way too hard for using in a 38 special, as I learned afterwards. I stuffed a piece of rag into the barrel, saturated it with Hoppe's No. 9 and let it soak overnight. the next day, I removed the rag and brushed and patched the barrel and it looked like new. Since I went to softer lead in the 38, it hasn't leaded since.
I also learned from the benchresters in the club that you should never clean the barrel on a 22 rifle. Apparently, once the barrel is fouled to a certain point, it stays that way and never gets any dirtier. Most 22 ammo have bullets which are also lubricated with an Alox lube of one type or another.
Generally, if you're only shooting the cast tumble-lube bullets (or any cast bullets with a good lube), in normal circumstances you shouldn't have to clean the barrel except maybe the chamber on occasion.