Hello,
Easiest way to go is by Bavaro Express, that's the bus which goes directly to Santo Domingo but they will drop you off in San Pedro.
Bad, bad advice.
do NOT take Bavaro Express, because it does not even pass through San Pedro (goes by the outskirts). Anyway, B.E. will NOT drop you off on the way anywhere (e.g. Boca Chica), unless you make very special arrangements with the driver, but I would not count on that. Anyway, it does not go through San Pedro so it's pointless.
Take SITRABAPU bus that passes in front of the hotel every 15-20 minutes. Take it to Bavaro terminal (about 20-30 pesos). You can also take motoconcho from the gate if you do not like to wait, for about 40-50 pesos.
Bavaro Terminal - take a bus to Higuey. Express, A/C bus leaves every hour on the hour so plan ahead. Other buses are local service with mostly no A/C. In Higuey you can take ANY bus that goes to Santo Domingo as all pass through San Pedro and will drop you off there. You can take regular or express. Buses leave every 15-20 minutes in peak times (during the day), every 30 minutes in early and late hours. First bus is at about 5 am and last one around 7.30 pm or 8 pm. Regular service, you pay the fare on the bus, express service you pay the ticket beforehand. Look for a guy getting paid in front of a bus or in a small stand by the platform. The only difference between regular and express service is about 5-10 minutes of travel time and movie on the express bus. All buses are comfortable large buses with A/C.
There is also a dedicated San Pedro service from the same terminal, but I would suggest you not take that one as there are older buses and most do not run A/C. Santo Domingo-headed buses will ALL drop you off in San Pedro.
When going back, you can pick the Higuey bus from San Pedro-Higuey terminal, or stand on the main road (e.g. at a big intersection) and flag down a bus that says Santo Domingo-Higuey. If they have seats available they will stop and pick you up.