I have always used the official cabs from the airport to get to hotel in Punta Cana.
There is a set fee ($35 to Paradisus Punta Cana) and they hold 4-6 people with luggage.
When you get to the airport and pass through customs and go to the right you see a large white sign with every hotel listed and a set feed.
The cabs accept USD.
Never had a problem.
However, if you want to book in advance, try going thru the hotel directly (not the miami Office)
Below is the contact and the fares I was quoted:
Genue Jimenez " email@example.com
PRIVATE ROUND TRIP RATES
PUJ -HOTEL US$.45.00 EACH WAY, FROM 1 TO 6 PERSONS.
PUJ -HOTEL US$.89.00 EACH WAY, FROM 7 TO 10 PERSONS.
PUJ -HOTEL US$.133.00 EACH WAY, FROM 10 TO 22 PERSONS.