I have anchored out in Bimini to get cleared. They tried to force me to get a slip. I told them I just need to be stamped, and I am gone, or I will clear in Nassau. They stamped me.
I have anchored, and taken a berth in Nassau. When anchored I climbed the wall at customs, and did my paperwork. They will come to the boat while in a slip.
Nassau is a good place to top off ice, and small items before the Exumas. Everything until Georgetown will cost a leg, and or arm in between. I would prefer leaving from Miami if Exumas are you destination. Less fight against the stream, and a much shorter distance.....i2f