Hi, Diznymagic,
We had the same question before our cruise (and OUR little one called it a baba, too!) and what we decided to do was take advantage of the difference in setting and routine to hope she would forget about it and "outgrow" it. That night when they got into the bunk beds, everything was new and different and fun, and when she asked for her baba, I said "Oh, there are no babas on the DISNEY SHIP! Isn't this FUN?!" and she was OK with that. She didn't ask for it again until the first night we were back at home and being tucked into bed. I said something about how she was a BIG GIRL now since she went on the DISNEY SHIP and there were no more babas, and just kept being firm, and it worked. She was a little sad, and I was a little sad, too, but it was as good a time to leave bottles behind as any.
If you are not ready to give it up, which is fine, remember there is no dishwasher in the stateroom, so either bring enough bottles, or bring a bottle brush and detergent and wash it in the sink. Have a great trip!