Hi Clarissa,
Your best bet would be to take a bus from your Resort hotel to the Magic Kingdom Theme Park and then from there, simply take the boat or Resort monorail over to Disney's Grand Floridian Resort & Spa.
To ensure that you get there in plenty of time, I would recommend that you are at the bus stop at Disney's Port Orleans Resort - Riverside by no later than 8am on the day of your dining reservation.
As you probably know, officially Disney's complimentary transportation is available one hour prior to Disney Theme Park opening time and up to one hour after Disney Theme Park closing time. That said, the folks at Disney are aware that many guests staying on-site will have made early morning breakfast reservations and the Disney Buses should be up and running in plenty of time to get you there.
My family have recently returned from a wonderful 7-night stay at Disney's Wilderness Lodge Resort and saw buses heading to all four Theme Parks as early as 7.00am on several occasions so if you are ready earlier, than 8am make your way straight over to the bus stop.
Wishing you a magical trip filled with memories which will last a lifetime!