When I was in Nassau back in 2007, a tour guide said don't bother exchanging your money. When I was there, $1 USD was equal to $1 Bahama Dollar. Both are widely accepted.
2007 - Majesty of the Seas (Bahamas)
2009 - Enchantment of the Seas (Western Caribbean)
2010 - Freedom of the Seas (Western Caribbean)
2013 - Golden Princess (Alaska, roundtrip from Seattle)