Can a dry p-trap in my laundry room cause a sewer smell in my bedroom on the other side of the house?
I rather suspect that you have a venting problem that is periodically forcing air back through the p-trap in your master bath. A venting problem can also result in the water of a given trap being sucked into the drain line.  When this happens you will get odors through that trap.  The likelihood of the restoring of water in another trap in the house affecting the traps effectiveness in your bath is almost nonexistent.