I would buy a Dewey rod with the correct sized jag,and cotton patches.A good powder solvent like shooters choice or Hoppes is required,and a copper solvent like barnes cr-10 should be used occasionally.You can certainly use a rod and clean from the breach toward the muzzle.You take off the jag and carefully feed the rod down the barrel to the chamber using a muzzle protector.Then you thread on the jag with a cotton patch by turning the rod,and draw the rod down the barrel and out the muzzle.
I do not use bore snakes,because it is far easier to change a patch than clean a bore snake,and I don't like running the same crud and residue through my barrel repeatedly.