Welcome aboard, Carey! You must be so excited to set sail in just a couple of months with Disney Cruise Line!
I always recommend choosing
Disney Cruise Line's Port Adventures versus booking through a different company. Why? Well, a few reasons. When you book through Disney, your group will meet onboard the ship and walk off together. So, no matter if the ship it a bit late into port, or if it takes the local customs officers longer to clear the ship for debarkation than usual, your group will be together onboard and ready to go. Secondly, when you travel with Disney's Port Adventures, the ship always knows where you are, so if the group is running late, the ship is aware and won't be leaving without you. When you're off on your own or with another tour company, you don't have these luxuries. Plus, Disney is tops in service. They just can't be beat!
That being said, guests are always welcome to leave the ship on their own to explore the port, or meet up with a different group. I can't guarantee that you'll make it to your 10:00 departure, but I don't think it should be a problem. If your all ashore time states 9:30, the ship it typically pretty close to that timing. The dock in Nassau is a long one, so you'll want to be ready to head right off the ship when it's cleared to be sure you are on time for your outside excursion.
I wasn't familiar with Rose Island in Nassau, so I looked it up and it reminds me very much of Blue Lagoon, which I adore. I'd encourage you to check out the
Blue Lagoon Beach Day as an alternative through Disney. My family and I have loved our visits there. It's a pristine beach with time for nothing but relaxing, or alternatively, lots of optional activities too, so check it out!
Happy planning, Carey!
Marcy