The roads in Nassau are very narrow and even riding in a cab scares me. HAHAHA Freeport is more wide open. You just have to be very very careful if you do that.
Call your cruise line and ask about wether you can bring your bike. I will tell you that if you do bring it, it will be in your cabin with you. Unless you have one of those little fold-up bikes, its going to take up significant space. Just a thought.
You may have to do more research to find a good bike rental place.
Have a great cruise.