Hey, Michael!
Welcome to the Disney Parks Moms Panel. When trying to get around Walt Disney World Resort the best thing you can do is take Scar's advice from Disney's The Lion King and "be prepared.".
The fastest, simplest and most direct way is to call an Uber/Lyft/taxi. It will take about 15 minutes and cost about $10-15 (prices subject to change). You won't have to worry about Walt Disney World Bus Service delays or transfers to other modes of transportation.
If you want to exclusively use Disney transportation then you will need to use
Walt Disney World Bus Service to Magic Kingdom Park then transfer to the
Resort Monorail. This trip will take around 40 minutes. The night before your reservation at
Disney's Grand Floridian Resort & Spa, please ask front desk Cast Member what time the early morning dining bus will pick up Guests for breakfast. They may give you a very early time because the bus may stop at another Resort hotel(s) after Disney's Saratoga Springs Resort & Spa.
Disney Dad Tip: There are no direct buses between Resort hotels in different areas. You will always need to transfer at a theme park. Disney recommends budgeting 90 minutes of travel time between Resort destinations. Resort hotels clustered in certain areas have their own transportation. For example, you may take a boat or monorail to some hotels in the Magic Kingdom Resort area. Cast Members can help you plan the best route.
Michael, enjoy making many
unforgettable Magical Memories!
~Jason ºOº