
Codrington Airport (IATA: BBQ) (ICAO: TAPH) Carib Aviation, [1]. Carib serves the airport from Antigua. Check in early--your flight may be overbooked (you may be stranded, or they may come back for you after the short flight to Antigua), or there might be an earlier unscheduled flight available.
The Barbuda Express, [2] offers ferries from Antigua. The ferry docks at River Wharf, some distance from the only town, but an easy walk to almost-empty beaches.