Caribe Tours (tel. 809/524-4952. www.caribetours.com.do, US$6.85 one-way) offers daily departures from Santo Domingo to Barahona and back, at 6:15am, 9:45am, 1:45pm and 5:15pm. Check schedules online or call to ensure there are no changes. It's a three-hour trip, with enough time for coffee stop when the bus unloads at Azua. Bring a cardigan or scarf as the A/C can get super cold on the bus. You'll get dropped off at the Caribe Tours office in the heart of Barahona city, close to many of the smaller guesthouses (although the city is not the place to stay in these parts). Check the website for the latest schedule in case of changes.
For more on getting around this region, see Moon Dominican Republic (Moon Travel Guides, 2016 edition).