Currently on probation for a misdemeanor conviction, want to travel on a cruise ship to the bahamas, is that going to be a problem? Do I need permission from my probation officer?

Most definitely otherwise you'll be leaving the state without prior permission and that will be an automatic violation. Don't chance it thinking "no one will know" as it's not going to happen that way.

You will need a passport of course but as long as the PO agrees to allow you to travel outside of the state and outside of the country , there should not be a big problem

How will the probation officer find out?