I looked into going to Bermuda back in Feb this year. I asked AA crew on crewstart what the BDA-JFK route was like on staff travel. Basically 1 flt daily 757 a/c used with evening dept JFK a/c nightstops and early morning dept BDA so aimed at business travel and it is always full.
Delta offer daily service between BOS and ATL to BDA.
Try looking at Air France...SkyTeam partner with Delta may have some deals.