I usually just use soapy water in the bore and then give it a swab with bore solvent, dry it with patches, then run apply a thin layer of oil. I also use a rag with solvent to get rid of the mess the primers left in the breech, as well as the breech plug. I would also suggest following the instructions on cleaning the bolt because it gets pretty dirty in there as well. Pretty simple actually, takes me about 15 minutes to do a good cleaning of it.
Evan