Welcome to the Disney Parks Moms Panel, David!
Thank you so much for stopping by to bring us your question. I know navigating your transportation options around the parks and resorts is important when trying to maximize your vacation time - I am here to help!
When taking transportation from Epcot to Disney's Hollywood Studios, there is bus transportation available at Epcot's Bus Transportation Depot near the main entrance. If you should find yourself in the Future World (front section) area of Epcot when you're ready to transfer, the bus will be your most efficient mode of transportation.
Bus transportation to Disney's BoardWalk Inn & Villas is not available from Epcot as this charming resort is a short walk or boat ride away from the International Gateway Entrance. However, you can take the bus to Hollywood Studios and then use the walking pathway along the canal to reach the Villa side of the BoardWalk Resort. Again, I recommend this option if you are in Future World when ready to transfer AND your Villa room is located nearer the Hollywood Studios end of the resort.
There is also boat transportation and walking paths available between these two magical parks near the International Gateway Entrance of Epcot, located between the United Kingdom Pavilion and the France Pavilion of World Showcase - please let me know if you should have any questions regarding these alternative options. Your best route will really be determined by your location within Epcot at the time you wish to head to Disney's Hollywood Studios.
I hope this information is helpful, David!
Have a magical day,
Faith