There was a thread about this awhile back. You might try a search to find it. I clean mine by soaking it in bleach and water; I've heard of others putting it in the washing machine. You might also consider tossing it after repeated cleanings--they're relatively cheap.
Wrap it with a rubber band and put it in the washing machine with some old towels you use in the garage. Hang it to dry. It will dry in just a few hours. Do the washing at the laundry mat if you like the relationship you have with your wife. ;-)
I have used John Galt's method quite a few times and I'm always surprised at how well it works. At the end of the dishwashing cycle, my Bore snakes look almost new, even though they don't get thrashed around like they would in a clothes washing machine.