What is the ruling on sleeping in a bed that is likely to have liquids – such as semen or other substances – fall on it after performing ghusl or purification, for fear of impurity?

The bedding does not become impure simply by intercourse. If it is touched by secretions, most likely they are pure maniy (seminal fluid), so washing it is only for cleanliness. However, if the impurity of madhiy (pre-seminal fluid) is confirmed to have reached it, then whatever it has touched must be washed if the bedding is intended for prayer; otherwise, it is only recommended. If the impurity dries and a dry object touches it, the object does not become impure. It appears that the questioner is afflicted with waswasah (obsessive whispering), and it is advised to refer to fatwas on treating waswasah regarding purity.