Below is the process recommended from Bartlein. LINK
Break in and Cleaning
The age old question, “Breaking in the New Barrel”. Opinions very a lot here, and this is a very subjective topic. For the most part, the only thing you are breaking in, is the throat area of the barrel. The nicer the finish that the Finish Reamer or Throating Reamer leaves, the faster the throat will break in.
Shoot one round and clean for the first two rounds individually. Look to see what the barrel is telling you. If I’m getting little to no copper out of it, I sit down and shoot the gun. Say 4 – 5 round groups and then clean. If the barrel cleans easily and shoots well, we consider it done.
If the barrel shows some copper or is taking a little longer to clean after the first two, shoot a group of 3 rounds and clean. Then a group of 5 and clean.
After you shoot the 3rd group and 5th group, watch how long it takes to clean. Also notice your group sizes. If the group sizes are good and the cleaning is getting easier or is staying the same, then shoot 4 – 5 round groups.
If fouling appears to be heavy and taking a while to clean, notice your group sizes. If group sizes are good and not going sour, you don’t have a fouling problem. Some barrels will clean easier than others. Some barrels may take a little longer to break in. Remember the throat. Fouling can start all the way from here. We have noticed sometimes that even up to approximately 100 rounds, a barrel can show signs of a lot of copper, but it still shoots really well and then for no apparent reason, you will notice little to no copper and it will clean really easy.
This is meant as guide lines only. There is no hard and fast rule for breaking in a barrel.