US Dollars are equal to the Bahamian Dollar 1:1 and readily accepted throughout the Bahamas.

The Casinos only use US currency. Shop keepers will take either. ATM's in the Casinos give US dollars as well as the ATM downtown near the Information Center. Most others will give Bahamian Dollars.

Most shops, Tours and restaurants accept credit cards and travelers Checks. The Straw Market as well as some smaller venues will accept cash only. 

You cant exchange Bahamanian money in the US or UK. The only way to spend it is to go back to the Bahamas.