There is no good or safe answer to this, at least not one that I have found. It is unlikely that there are any safety belts available for installing your carseat on any of the buses/taxis. You might get lucky, but I think that would be the exception rather than the rule. For trips such as these, that is about the only time the Cosco Tote-N-Go carseat might be a safe alternative.
http://www.carseatdata.org/TNG.html
This is less than an ideal carseat, but better than nothing and small and lightweight to carry around.
Statistically, unbelted passengers in busses are safer than properly restrained occupants of cars/taxis (for a myriad of reasons), so for the
DCL excursions, I prefer buses to taxis. If you do use a bus, it is best not to have your little one in your lap (they become your airbag in a crash), but right next to you in their own seat. I've had some dirty looks when my 4 year old is occupying her own seat, but she did pay for the excursion like everybody else and it is unfortunate that the excursion companies seem to overpack the buses.
I always have left my carseat back in my cabin during the excursions (but I am totally tense during transportation, I would prefer to use the carseat!). However, I would always use the carseat in the US for taxis and rental cars (where I am assured of having a seat belt).
With a toddler, the most overlocked item to bring on the excursions (in my opinion at least), is a small, umbrella folding stroller that is decent! Steering is important while walking through town, sometimes the walkways are less than ideal. Also, bus space is usually limited, so there isn't really room for larger strollers. This also comes in really handy for the young ones on the cruise. You want a stroller with a narrow footprint, because the elevators can get quite crowded. And there the smaller fold is really helpful in the small rooms. I think I'm bringing my Mac on my next trip. The hood leaves something to be desired, but it does have a rain cover, which is really nice for these tropical areas.
Have fun,
Jennifer