I clean every 10 to 15 rounds. That helps to keep the copper build up at bay. I also go a round with JB every 100 rounds.
As for checking the bore for copper short of a bore scope there is one little trick I use. After cleaning and drying the bore push one last clean patch up the bore but stop about 1/2" short of the muzzle. Hold the muzzle up to bright light or use a flash light to look into the bore. The White patch will reflect the light and let you see the lands and grooves pretty good, you can see even more with a magnifying glass. You can also use a clean dry Q-tip inserted into the muzzle a bit and shine a light in behind it, just rotate it around to look all the way around. If you see any copper in the muzzle you can be assured it is all the way through. Down side is you can still have some copper in the bore but not see it at the muzzle, but like I said short of a bore scope, I think it is a pretty good indicator anyway.
I took a mini mag flashlight, Q-Tip and a magnifying light to a local gun shop recently to look at a used Savage/Anschutz Target model 22rf. When I did this in the shop the 2 guys behind the counter, and 2 other customers, asked me if I was going to take its temperature next, and they all had a puzzled look on their face trying to figure out what I was doing. I asked them if they had not seen that done. They asked me what the heck are you looking, so I told them I wanted to look at the crown and the lands and grooves to make sure the rifling looked good (since it was a 22rf I did not think it would have copper) so I showed them, and they were amazed at how much of the lands and grooves you could see that way. Bad thing is the 2 guys have worked there for at least 20 years and you would think they had seen that little trick.
Give it a try, you might be surprised how well you can see in there this way.