At this time simply there is no public transport to Puerto Plata.
The nearest you can get is to the exit to Navarete. At the former "rotonda" crossing is a small but good, safe and recommended hotel "La Rotonda". About 20 USD, some rooms with air condition, TV. Fast food and car wash near by. Also they have a parking lot. Stayed there several times to not go the route to Puerto Plata / Cabarete at night when I was late.
The busses to Puerto Plate start early about 6 a. m. opposite the street. Just ask, most people know. Be sure to take an "Expreso". From the arriving place in Puerto Plata, Caribe Tours is near within walking distance (or the minibuses) to go further. From Hotal at "La Rotonda", a Caribe Tours station is not far away (there are 2 in Santiago).