Semi, you really need to scrub the bore to get it fully clean. A good quality nylon or brass brush won't hurt your bore, like earlier said. Also, get yourself a good, one piece, coated rod and a bore guide. Damage to the crown is much more likely than damaging the bore.

For copper, I use a concoction that the gun shop I frequent mixes. It's potent, and you better have air circulation, but it works great. They won't tell me what it is, but it's probably a combination of Sweets, Shooter's Choice, and raw alcohol. LOL