For what it's worth....I use a bronze or copper brush with Hoppe's #9, then push a piece of paper towel (with dowel) thru barrel a few times. I may then wet (with Hoppe's)a piece of towel again and push thru. Again dry paper towel.
A piece of paper towel works it's way into the lands and grooves much better then a piece of cloth.
Bounty stays together better then some other brands.
Sorry should have posted under previous barrel cleaning thread of Jan 25