I dare say the reason you were put through the id hoops on commercial carriers was because you were on commercial carriers.
If you want to leave the US for the Bahamas just leave. The Bahamas doesn't care if you cleared out of the USA. Be forewarned - other countries do not necessarily feel the same way.
The important thing to do for the Bahamas is to make sure you have all the bases covered as to what is required to get back into the US. Your life will be a lot simpler if you are aware of what's necessary beforehand.
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