Always clean, oil, and check screws to make sure they are not loose. EVERY TIME YOU SHOOT.
If you put the barrel across a table , or counter top, with the barrel down, and the stock up, any water that might run out the bore, or vent hole will drop, and drip, down , and not over your stock or other gun parts.
You can plug the vent hole, and then carefully pour water down the barrel, with some liquid soap added, then run a bore brush down to break free any crud stuck in the corners of the rifling grooves. pour the stuff out in to your sink, or toilet, and then rinse the soap out a couple of times too.
Then you can dry the barrel with clean dry patches, followed by oiling it. Then clean and dry the outside of the stock and barrel, and oil or grease it for storage.
Patches should come out of your barrel as clean as when they went in, if you have cleaned the gunk out of it. I don't hesitate to blow down the muzzle when the water and crud have been poured in to the sink, holding the gun so that the vent hole points down into the sink. This removes a lot of the water left in the barrel, and clears the vent, too.
Just don't hurry in cleaning your gun. Let the soap and water SIT for at least 1/2 hour to do their thing. Don't rush it. Its like putting soap and water into a pan that has food baked onto its sides. Hurry it, and you end up scraping the crud off with a spoon, or coarse brush or pad. Let it sit for a half hour to an hour, to let the soap do its chemical thing, and you pour the crud out of the pan. It works the same with cleaning barrels.
The soap works to emulsify the carbon deposits in the barrel, after the water has dissolved the salts of Nitrate, and Sulfur, left over from burning BP in the barrel, which are poured out with that first dirty wash waste water. It takes time for that to occur. Give your soap time to work. Let it do the heavy labor for you. :shocked2: :hmm:
Remember that water is a natural solvent. It does NOT have to be boiling hot. It will dissolve the crud all by itself. The soap simply helps to break up the carbon deposits, and float them in the water for removal.
Use Tepid( skin temperature) water to avoid flash rust from using water that is too hot. For short term storage, WD40 ( water displacing oil formula #40) does a pretty good job. For long term storage, consider a product like "Sheath". But, nothing beats checking our guns every week and giving them both a dusting and a new coat of whatever- oil, wax, etc. you use to protect them from rusting.