You can take either of two. Depends on where in Romana you need to get off. If you need to go the the center, Sichoem is better. If it does not matter, take Sichoprola.
For Sichoem, ask to take the Expreso bus. If not, you would end up takinga small minubus where your luggage would not fit and you would not ride comfortably. Expresos are large buses with A/C.
For Sichoprola, you can take any bus, as all are large and most have A/C (all Expresos and most of non-expreso buses).
Parque Enriquillo is at between street Jose Marti and Duarte, with Ravelo crossing. Just off Avenida Mexico. Just ask the taxi driver to take you to PE.
Ask them to take you either to Romana or Higuey bus stop (Parada de La Romana or Parada de Higuey).
Buy the ticket and board the bus.
Ticket price would be around 120 pesos, give or take a few.
Hours of departure - from early 5am till 7 pm sometimes 8pm.
5am to 7pm you are always fine.
trip duration - about 90 minutes.