Earlier you could have taken a taxi who would have dropped you off at the bus stop for the bus to Higuey. But forget about it if you arrive at 7 pm, which means you will be out of the airport around 8 pm, to late to catch this bus.
Suggest you take a RD$350 taxi into Santo Domingo and overnight in a hotel in the Colonial City. Next day take the Sitrabapu RD$120 bus to Bavaro bus stop (bus departs at 7 and 4 pm). Will cost you about RD$300 more for the taxi to get to your hotel in Punta Cana.
Elsewise, the RD$1,900 fare the taxi will charge from Las Americas to Punta Cana is your best deal. This fare may be higher because of the late hour. The taxi driver may have to overnight out there so as not to have to drive back home at that late hour.