You are right about some dark colors transferring - even after being gently washed once. (Experience speaking here! )
You are lucky to be able to have a spare bed to lay them out on. That is probably "the best" way to store them. Assuming you do not have cats that think that any horizontal surface is theirs! (lol).
My cats seemed to have a "hair release button" that activated as soon as they got near anything made of fabric.