I've heard from a few people that shoot .22 target rifles that a Bore Snake is the best method of cleaning because a certain degree of fouling is needed to keep your barrel accurate. This is why I never scrubbed my 10/22 target rifle I built and have a used a Bore Snake from day one. I can still to this day shoot 10 rounds at 100 yards and cover the group with a quarter using a cheap Butler Creek barrel and mostly stock 10/22 set up.
I spray the first section (right before the bristles) of the Bore Snake with CLP, then drop it through and pull through the muzzle. Twice is the norm.
My ideology is that the first part soaks the bore, the bristles clean, then the tail end dries.
I should also add I'm shooting Wolf ammo. Its really hands down the most accurate .22lr ammo I've ever shot.