Do cat fleas spread on people?
Cat Fleas certainly do spread on people! One pregnant female flea can lay up to 1000 eggs. If your cat comes in with one pregnant flea, they aren't all going to stay on the cat!!
If it doesn't have fleas, nothing.If it does, there is a possibility it would spread to the bed but fleas prefer living things so they can remain on the cat. But if the cat has fleas and it is left unchecked, there is a chance the house with become infested with fleas -- especially if there is a lot of carpeting and soft furniture. Other animals increase the speed of infestation.