We loved Bimini!!! - went in March prior to fishing season and it was perfect. It was safe and people were very friendly. We loved the hotel; however, rooms are over a VERY loud bar (whether people are there or not) so call and ask what nights they play music and avoid those. The place is adorable - nicely decorated, great views, across the street from liquor store. Rent a golf cart to explore the island. A 5 day stay in Bimini would be perfect - avoid jellyfish season if you want to go in the ocean. Good snorkeling off the shore, better snorkeling/diving on trips from Big Game. Water rivals any Virgin Island (although Bimini is part of the Bahamas).
If we go again, we'd stay at Big Game - more expensive, but better amenities, great restaurant and central location.