RE: How do you break in a new rifle?
When you are breaking in a barrel you can not worry about groups. You have done well ,but the barrel will take closer to 50 - 100 rounds to be broken in completely.
you can work your way to cleaning after 5-7 shots if you are not getting copper fouling.
If you do want to try for a better group ,after a good cleaning push clean patches thru until you see nothing on them ,then fire a fouling shot off to the side of your target then shoot three more and check you size .
Good luck