DANG!
Use boiling water to clean the whole barrel on the outside - that will remove all the oils - then while the barrel is warm apply cold blue - use a very fine steel wool and rub itin - usecircular motions - let itdry then clean it off with a lightly oiled rag to remove the excess bluing - repeat the process to get a deeper blue...
Here are a couple cold blued barrels I did way back when...