We're just back from the fort and can speak to strollers and transportation!
We had a double BOB stroller as well as a single umbrella stroller for our four children ages 6,5, 4 and 2. We didn't have any problems getting the strollers on and off transportation.
The bigger boats that go direct from FW to MK require you to fold down a double stroller, but not a single. There were many single strollers parked inside towards the front of the boat. The smaller resort to resort boats require you to fold down all strollers. The captain told us that strollers are required to be counted as a person in the head count of boat passengers on the smaller resort boats! We rode these smaller boats the two mornings that we left early to go to MK (via the Contemporary) and folded down our strollers and loaded them on. The boats were virtually empty at 0700 so there was plenty of room and we didn't feel bad taking up the seat space.
One thing we didn't really factor in was getting our strollers and peoples down to the marina in our golf cart. We had to make two trips. The first to take the strollers down to the docks and the second to bring the family

No big deal. It just took extra time early in the morning. Might not even be an issue for you though...
We only road the buses a couple of times with strollers. They were only crowded once and no one seemed to care about the folded up strollers. They just took up aisle space.
Definitely bring your BOB for your little one. They are heavy and bulky but so comfy and easy to maneuver. Our umbrella stroller was tricky to move through crowds and difficult over uneven ground in the parks. The BOB was smooth riding for both the kids and the adult pushing.
Have a wonderful time at FW and in the parks!!!