Generally, US Customs are only picky about drugs, and immigration visas.
A few extra packs of cigarettes or bottles of booze is not their concern.
It is generally less expensive in US retail stores anyway.
Stay on board of the plane, door closed until gestured to open the door.
Have the passports and GD (manifest) in hand.
Remember, the I-94 visa waiver (green form) not approved for private flights.
Regular visa (white form) I-94 required for passengers. Crew visa required.
Get the forms ready prior to arrival if you can.
Handlers often have a supply of such forms available in the Bahamas.
Do not forget the timely notification of ETA as per their regulations.
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Have a good flight -
Happy contrails