It leaves from Caribe Tours in Charamicos at about 3:30 and stops to pick people up along the way and still gets to Santiago in about 2 hours. You pay on the bus. The bus is similar to Caribe Tours bus but isn't, and it's cold so wear a jacket.
There is also a nus who leaves from the police station in Puerto Plata (to Santo Domingo, but stops also in Santiago I think), they leave at 3am.
But then you have to get to Puerto Plata first....