I went to Atlantis twice last year. I went fishing offshore with these guys both times.
http://www.chubascocharters.com/There was a thread last week from NW80 (I think) and he is fly fishing (I think) in the bahamas now. He started in Nassau and took a charter out to another cay.
I never saw any one fishing from atlantis or any of the hotel beaches, from what I saw. It seemed to me like the beaches were generally public but access to them was not particularly easy as you had to make your way through the hotels to get there. Basically, I think the law says they are public, but they make it hard for the locals to get to them in front of the resorts. There is atleast one public park with a beach about 5 to 10 minutes cab ride from atlanits that I would suspect you can fish from. I have no idea about license or whatever. They never asked for one and we did not have one for going offshore. I am sure you can find more info on the internet if no one else here has any advice.
Atlnaits is a cool place. Let me know if you have any questions.