The taxi will be expensive, about US$90. You could rent a car for less. It is a two hour drive to get from Punta Cana Airport to La Romana (Dominicus) area where your hotel is located.
You can go the way the locals get around and take a Bus to Higuey from the Bavaro bus terminal (will cost you about US$20 for the taxi to the terminal). The bus from Bavaro to Higuey is about RD$25 (less than US$2) and the bus to La Romana will be another RD$25. But the taxi to your hotel will be another US$40, so the hassle is not worth it.
First option, I would try harder to get a ticket into La Romana Airport. Your hotel would be so close.
If you have to fly into Punta Cana, I would switch hotels and stay at a Punta Cana/Bavaro hotel.
If not, I would suggest you rent the car and check out the sites on the way. the car will give you the liberty of touring the Ponce de Leon house, the Basilica de Higuey, also Altos de Chavon. Check out our travel pages (see Bavaro/Punta Cana, La Romana, Juan Dolio pages) for attractions that will be within your area.
