It's not a straight bus ride to Punta Cana from Puerto Plata. You would have to take a bus from Puerto Plata to Santo Domingo. Transfer to another bus from Santo Domingo to La Romana. Then in La Romana you would have to take another bus to Higuey. From Higuey you would take a differnt bus to Punta Cana. It's a long trip.
You may consider by plane because the flight from POP to PUJ is approximately 50 minutes.