Wash it in the sink with soap and hot water and hang it up to dry. Some people put them in an old sock and run them through the washing machine, but I don't put lead contaminated cleaning implements in the wash.
I use a simple process, Very HOT boiling water, Simple Green (about 5 sprays), soak for about 15 to 30mins., rinse and hang dry in the garage. Looks and feels as good as new..
When I first got my boresnake I was looking on Amazon for those small zippered bags to throw in with your laundry, then I thought to myself why would I want to wash it with the rest of my clothes.
I am going to try the sink and Simple Green method mentioned in this thread when it is time to clean it.
So far I have only cleaned my 22 once with it, so I am sure it is good for a few more snakings before it gets cleaned.
Its a free country you are allowed to wash your snake any way you want and as often as you like.
I wash my bore snake in the washing machine when i wash a load of shop rags. Not with clothes... the wife wouldn't like snakey clothes, but with the dirty rags it's not a problem.