I'm a law enforcement firearms instructor, armorer and served for 12 years in the Marine Corps as a Scout Sniper. Don't worry about copper fouling. In fact, don't stress about cleaning your bore. Most people do more damage to their rifles in cleaning them than they do shooting them. Something most people don't expect to hear from a sniper is that we shoot dirty guns. I'll go 250 rounds or more before my bore even sees a patch. I rarely (can't remember the last time I did) used a brush and if I did, it was nylon and not metal of any kind.
The subject of cleaning rifles creates consternation on par with your friend finding out that you're dating his mother. I'm not here to tell anyone what to do or piss in anyone's Cheerios, but most people clean their rifles way, way too much. Understanding that every rifle is different, there comes a point where your rifle will begin to suffer accuracy loss and that's when it should be cleaned (being dropped in saltwater or dragged behind a truck not withstanding). Try cleaning your rifle meticulously and then shoot it without cleaning the bore until you see your groups opening up. You'll be quite surprised how long that is. Another tip: Do not clean your rifle with a sectional cleaning rod. They are notorious for scratching bores. When I do wet patch my rifle, I use a product called Shooter's Choice MC-7. It can usually be found at Walmart. It's cheaper than whatever the latest, greatest product made from unicorn tears or dragon saliva happens to be and it works.
A great article was written several years ago by the late Chief Warrant Officer of Marines, Pat Rogers. For those of you unfamiliar with what a CWO is in the Marine Corps, he or she is a Subject Matter Expert in their particular field. In Pat's case, he was a small arms expert and served for a time in the Foreign Materials Acquisition Exploitation Unit (a unit that "finds" enemy weapons and weapons systems in order to test and examine them). He was also a Distinguished Expert rifle shooter and NRA High Master Rifle. In short, he forgot more about rifles than you know. The article is about keeping an AR weapons system functioning, but it applies to most, if not all rifles. It is canon amongst riflemen:
http://www.slip2000.com/blog/wp-content/uploads/2012/06/keepitrunning1.pdf