When you are niddah, it is not permissible for your husband to sleep in a bed designated for you. Therefore, if the single bed is designated as yours, he cannot sleep in it. It is possible to reassign the bed, ideally by having him sleep in the single bed for three nights in a row while you are tehorah.
During the time that you are niddah, you may sleep on your side of the double bed as long as your husband is not in it.