Literally, “to bleed one white” is to cause one to lose so much blood that he becomes pale, but for the past three hundred years men have been said to “bleed” when they have unwillingly or through fraud parted with an undue sum of money, as through blackmail or the like.
When the victim has been “bled white,” in modern parlance, he has paid through the nose to such an extent that the extortionist sees that his racket has come to an end.