On the buses that run internally, ie from park to resorts, there is no place underneath to store them. You need to carry them on the bus with you, folded up.
(ME buses do have a space underneath for the strollers and other things.)
Not sure how old your child is, but it might be worthwhile to buy a cheap umbrella stroller to bring on your trip. Larger ones can become a pain after a while.
We've brought the full size strollers before and they take up a whole seat or enough room for a whole person. They are also harder to carry on the buses, esp when people are already seated...I was always afraid of hitting someone with it. Plus they are heavy. We've also used the smaller strollers too and they can also be cumbersome for many of the same reasons.
We now have a Mac, which is great. It folds up as small as an umbrella stroller and we can fit it between DH & myself in the seats. It's very light to carry. It also has a strap for carrying in on my shoulder so I can grab anything else that needs holding (toddler, shopping bags, etc

) I know there are cheaper umbrella types that also have this feature.