The boat goes to the Swan/Dolphin, Yacht/Beach, and Boardwalk before going to the World Showcase at Epcot. You can roll the stroller right on. Boats run every 10-20 minutes, and it takes 30 minutes for the complete trip.
There is also a DIRECT bus from the front entrace of Studios to the front entrance of Epcot that runs every 15 minutes, and takes 10 mins to get there. Strollers must be folded.
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