This feedback posted by SV Gallivant elsewhere on the site:

GRAFT—NASSAU CHECK-OUT
We called to see if we could check our sailboat out of the country at Nassau Harbour customs. No answer.

We walked up to the office, which was behind a locked gate.

We asked the uniformed guy at the gate if we could check our sailboat out of the country there the next day. He told us we should check out through our marina. We told him we weren’t in a marina. He recommended we go to a marina to handle check out. We again asked if we could check our sailboat out of the country there. He was discouraging but said if we wanted to try, we should get there early because the area was likely to fill up with construction work. There was also a cement wall we weren’t too keen on tying off at, as unlike at a marina, we knew we wouldn’t get any assistance and were concerned about surge. The concrete wall seems to be in fair condition with two medium-sized bollards to tie off to.

We decided to check out via Nassau Harbour Haven, coming in only long enough for checkout ($1/foot+tax).

Upon arrival, Nassau Harbour Haven contacted customs. About 1 ½ hours later someone from customs showed up and boarded our boat. After she went through the paperwork, she said we owed her $50 because customs had to come to us.

We said we tried to go to the dock initially and were discouraged. She said we talked to the wrong person.

As we dug for $50, and only came up with $49, she said that was ok. She refused to offer a receipt for the payment.

We told the folks at Nassau Harbour Haven and they said customs was not supposed to charge us. They said this is not the first time it’s happened, and they report it when it does, and encouraged us to do that. They also said they would report it to the office of tourism and encouraged us to do the same.

Bottom line: If someone from Bahamas customs tries to charge you for exiting, refuse to pay it, or, at least refuse to pay it until they hand you over a receipt on your amount of payment.