That is considered the high season, but you can try ANSA. I was able to get them through expedia on my last trip. There is an office at the airport on the outside arrival area. They are linked to Europcar and probably other car rental companies. You also can do searches on the web for car hire Barbados. In recent trips I have seen some local car rentals align themselves with larger car companies, and this should make the price better. ANSA was the first of such rentals for me.
