Take taxi for 3-5 minute ride to Las Americas ($10 if you ask a dispatcher inside the airport, maybe less if you go outside of the airport and haggle w/one of the drivers). Tell the driver where you're going. The drop-off is the same for all bus destinations, but he will make sure that he communicates your intent to the dispatcher at the drop-off.
Note: The dispatcher will wear plain clothes (possibly dressed down), i.e., he might not appear to you as what he is. Make eye contact and stay close to him. He will make sure you catch the La Romana Bus (100+ pesos DR, around $4 US).
Getting on the bus tell the driver and conductor both about Be Live Canoa. They will drop you as close to there as possible where you will probably have to take another taxi for a short distance.Good luck.