Hello Ian, and welcome back to the Disney Parks Moms Panel!
Getting around the Walt Disney World Resort is quick and convenient when you hop aboard Disney Transportation. From the monorail, to boats, to buses, you can find just about any mode of travel you like to get where you want to go.
The Transportation and Ticket Center, or TTC, serves Guests who are accessing the Magic Kingdom from the parking lot via monorail or ferryboat; Guests traveling to one of the Resort hotels along the monorail loop; and those who are transferring to the Epcot monorail. The TTC also serves Guests arriving via charter buses and the Orlando LYNX city bus system. At this time Walt Disney World buses don't connect to Theme Parks from the TTC, so you would need to head to the bus hub just outside the Magic Kingdom for direct service to all of the Parks, or jump on the monorail to one of the Resort hotels to board a bus there.
I hope this helps in your planning, Ian. Please stop by and see us again if you have any more questions, and have a magical Walt Disney World vacation!
Keep Disney Dreaming,
Kathy