You have two choices for an express bus to Santo Domingo -- Metro and Caribe Tours. One will bring you to Leopoldo Navarro Street in Santo Domingo, the other to Av. Winston Churchill (in front the Plaza Central, the largest Santo Domingo shopping center). My personal preference is Metro Bus.
Metro Bus (Tel. 586-6062) Calle Beler corner Calle 16 de Agosto has six departures from Puerto Plata.
Caribe Tours (Tel. 576-0790) Calle 12 de Julio corner Jos? del Carmen Ariza, has 12 departure times.
Buses leave from 6:30 am to 7 pm. Unless you are traveling on a holiday or on Sunday afternoon, you surely will find space on one of the departure times. If you miss one bus, just catch the next. Buses leave on time so you should arrive at least half an hour prior to departure time.
Bring a jacket or sweater as the buses have strong air-conditioners.