I think you will probably have to go through Gatwick with British Airways, for example -
Depart Dublin British Airways (DUB) Stop 1 London Gatwick (LGW) Grantley Adams Intl (BGI), total travel time around 12-13 hrs
American Airlines do a 1 stop trip also, but you might find a direct flight with a charter.
yes i have been going to barbdos since 1996 went with aeroflot then and it was a direct flight.you ca go to gatwick or manchester with virgin airlines.I find them the best rhey are scheudled flights and go on time.1 years ago i went with excel airways much cheaper option because i was going for xmas.unfortuntaley big delays but check the uk site out,They have some good paxkages for flight and hotel for june 08.Butterfly beach hotel vey basic, discovery bay west coast ok hotel.I must say i go to barbdos a lot and there is a major difference in the prices travel agents give,Joe waslh tours total ripp off.I find sunway is the best.I think the site is xl airways .com.