The fastest way: Take the bus to MK and take the motor boat from there to the GF (the boat goes directly to GF. The monorail has 3 other stops). The monorail is recommended if the weather is bad.
I'm not clear on when the transportation starts running from the resorts. It is either a half-hour or a full hour before park opening.
The fun but not fast way: Walk through Epcot's International Gateway and go across Epcot to the entrance. Take the monorail to the TTC. Change at the TTC to the resort monorail and ride to the Grand Floridian. Obviously this will only work if you 1) have an annual or park hopper pass for accessing Epcot; if it's a park hopper you should plan to visit other parks during the day; 2) have plenty of time to spare; 3) don't mind walking.
If you are in a hurry, or want more control over when you leave and when you get there, the cab from the BC is the best option.