I stopped using steel wool it leaves to many fines that rust as soon as you look at them
Remove the breech plug if you can
Use Scotch Brite pads cut in sections ,round like a patch so it fits over a smaller jag . tight enough to fit the bore since you want the patch to follow the rifling twist
I made up a jag that has rubber washers on either side of the pad. Many times I'll use a leather washer and fine lapping compound.
Mark you rod so you travel the full lenght of the bore
Use a muzzle protector ,bore guide
Use a good heavy oil
Run the pad in and out 100 times
Clean
Go shoot and see how the patches look
Remember you may be shooting to tight a patch ball combination
Bronze wool works well also
Here is a link to 3M
Scotch-Brite™ AbrasivesAs stated previously shooting a 100 or so shots will also clean up the rifling edges