I've frequently switched between copper bullets and conventional bullets and there is no loss of accuracy as long as the barrel is cleaned properly. Also, the newer Barnes TSX bullets don't foul as badly as the older Barnes bullets that didn't have the circumferential grooves.
As for cleaning:
1. A number of products work well in getting copper out but my choice is Wipe Out since it works very well and hasn't caused any rust in my barrels even when left in for a day or two or three. You shouldn't leave ammonia based products in a barrel for a prolonged period as they will cause corrosion.
2. Rubbing of a steel cleaning rod on the bore can damage rifling. I use coated or nonmetallic cleaning rods.
3. Never use a stainless steel brush to clean; only use a bronze brush or Nylon brush as you want to use something softer than steel to avoid bore damage. Actually, I rarely use brushes; just patches and Wipe Out preceded with Wipe Out Accelerator.
4. If you oil the bore after cleaning, be sure you remove all oil before shooting. I don't use oil in the bores of my firearms. The last coats are usually with Prolix followed by a dry patch or two. Prolix won't cause the first several shots to be high as will an oiled barrel you haven't removed the oil from. I also sometimes use Microlon Gun Juice for the last coats.
