A .22 I may clean the barrel when its new for 1 -2 shoots then leave it alone .
Any centerfire Barrel only cleaning were talking about here.
I clean from Crown to chamber I lay in some foam cleaner ( Hoppes NO 9) I have a tube longer than the barrel that I fit to the Spray nozzel and then leave it to work for 10 min .
Then All from chamber to crown patch it out may take 5 - 6 patches then run the bore scope up and look for any copper If any I will use sweets have another look after more patches if it stubborn i will use a Gunsmiths Brush with sweets but only I pass, patch and have another look .
JB bore paste and polish I will only use on a second hand firearm I have just bought just t make sure its realy clean Its My Personal opinion with JB it is a lapping paste when all said and done..
I did one time try all of the above on a .22 mag that would not clean bought it from a guy in southern NSW I ended up fire lapping that clean