I think you can do it this way:
Create the billing address fields first, then bind them to the ship-to address, then make the ship to address hidden.
Then run an action so that if the yes check box is marked then the ship-to address fields become visible.
Create another set of ship-to address field that are not binded to the billing address fields and hide them.
Run another action so that if the no check box is marked, then those ship-to address fields become visible, and they are empty.
It should work that way.....however, there could be another way to do it that is easier, I don't know.