COPA and Aeropostal fly twice a day, one stop, from SDQ to Bogota, Colombia. Cheaper way, Avianca departing from Punta Cana (only on certain days of the week), nonstop flight.
TACA starts flying to and out of SDQ in April, I bet they will have a connection to Bogota and other south american cities.
Of course you can fly AA, Lan or almost any other airline with more stops, longer layovers and/or more expensive tickets.
Bon voyage
Jess