Hi Frank!
Welcome to the Disney Parks Moms Panel.
There is boat transportation available from
Epcot to
Disney's Hollywood Studios, but the FriendShip Boat can only be taken from the International Gateway entrance to Epcot. This is located in World Showcase, between the France and United Kingdom Pavilions -
see a park map here. The Epcot monorail is stationed at the main entrance to the park, so if you arrive at Epcot by monorail you will have to walk through the park to reach the International Gateway. You have a few other options - you could take a bus to some of the Disney Resort hotels:
Disney's Yacht Club Resort,
Disney's Beach Club Resort and
Disney's BoardWalk Inn. These Resort hotels are within walking distance of the International Gateway, but you wouldn't even have to walk to the International Gateway entrance because you can take a FriendShip Boat from these hotels to Disney's Hollywood Studios! Disney Buses run to the Disney Resort hotels from all the theme parks, water parks and Disney Springs. However, there is also a bus service that runs from the main entrance to Epcot to Disney's Hollywood Studios, and the bus stops are located close to the monorail station, so you would not have to enter the park if you opted to take the bus.
Please come back and visit us if you have any further questions. We will be happy to help you plan your magical vacation to Walt Disney World.
~ Sue