This is my first BB and hopefully it'll get the ball rolling as I've got several that I should be able to pick off easily if I can find the time.
I have made the mistake of washing our napkins with our clothes a time or two, with some clothes getting grease spots as a result.
Despite this I somehow hadn't thought to devote a bag for them until coming across this BB.
So our system now is to place the dirty napkins in the bag shown below. When it's full, also pictured, they get washed on a sanitary cycle and then returned to their spot in the drawer by the oven mitts and pot holders, last picture.