Hi Amy,
It sure sounds like you have a great first day planned. My son loves nothing more than heading straight to one of the Disney Water Parks as soon as we arrive at the Walt Disney World Resort.
In general, the complimentary
Walt Disney World Bus Service does not travel directly from any Disney Theme Park, Disney Water Park or Disney Springs to another.
You will however be pleased to hear that there is one exception. Disney's Typhoon Lagoon has it's own unique bus service. The morning bus service stops at Disney's Typhoon Lagoon before Disney Springs. Between 11:00 AM and 2:00 PM, the bus service stops at Disney Springs first. After 2:00 PM, the bus service to and from Disney's Typhoon Lagoon Water Park is only available at Epcot.
This means that if you want to go to Disney's Typhoon Lagoon Water Park after 2:00 PM, you will first need to go to Epcot and then change onto the bus to Disney's Typhoon Lagoon Water Park. Likewise, on your return journey (if after 2:00 PM), you will be dropped off at Epcot, and from there, will need to transfer to another bus or monorail to get back to your Disney Resort hotel.
As you are wanting to go directly from Disney's Typhoon Lagoon Water Park to Epcot in the afternoon, this works out perfectly for you.
Obviously, bus schedules can change at any given time so if you are in doubt at all, I would recommend that you confirm what the current situation is with a Cast Member when you check-in at your Disney Resort hotel
Wishing you a magical trip filled with memories which will last a lifetime!
Emma