What is the best bedding for shedding dogs that won't ruin my washing machine?

We use blankets for our dogs to sleep on and they are always coated with dog hair. I usually hang the blankets on the clothesline on a windy day to help remove some of the hair before I wash it, but now that it is winter that’s not always possible. How do you cope with washing bedding that is coated with dog hair? I don’t want the washing machine to get clogged with the hair.