A taxi will run you $35-$40 one way, so this is the way to go.

Have a cab driver to take you to the Expreso Bus (Gua Gua, pronounced Wa-wa) to Boca Chica. I had read that the station was at Parque Enriquillo, but I didn't see a park where I was dropped off. Make sure you specify you want the expreso, I haven't been on the other but I assume it takes longer.

The bus will leave once it fills up, when I went it took about 15 minutes on a Monday early afternoon, but could take shorter or longer depending on when you arrive. A guy will collect your 70 pesos during the journey. There will be a lot of stops along the way, I would estimate about 20, but it should take roughly 30 minutes. The dropoff is at Parque Central near the corner of Juan Bautisa Vicini and San Rafael. They don't make an announcement, but unlike the earlier stops it seems this one is a major stop and they'll wait there a while.

To return to Santo Domingo, go to the same pickup location. The Gua Gua should take you to the main station for no charge. From the main station you'll take the expreso back to Santo Domingo for the same 70 peso fee. The return ride early Monday evening took almost an hour. They should drop you off just north of Parque Independencia.