If so, take a taxi to Caribe Tours in Santo Domingo and hop on the bus. I don't know how many people you are but the bus in less than 10 US per person (someone that used Caribe Tours recently might come along and post the exact price). This is of course providing that you arrive before the last departure which I believe is around 6 or 7pm.
For $100 US or less it just won't happen. Do as suggested, take a cab to Caribe or Metro and take the bus.
Will you also be flying out of SDQ for your return flight home?
What time do you arrive at SDQ and what time will you have to depart SDQ?
Sorry to say but if Sosua is your destination of choice it probably would have been better to spend the extra cash and fly into POP (if a flight is available). You will easily waste way more than half a day each way traveling SDQ to Sosua.