Hi James,
Ah, what a fabulous trip you have planned!
The Villas at Disney's Grand Floridian Resort & Spa are so elegant and lovely, and a trip over to
Cape May Cafe at Disney's Beach Club Resort is always a treat!
Although there may not be theme park buses running at the time of your reservation considering the early hour, there are often early buses running at Walt Disney World for just this reason - to get guests to character meals. I suggest that you stop at the front desk of your resort the day before your reservation and mention your reservation time and where you are going. The cast member there should be able to help you out and let you know the time that a character breakfast bus would leave on the day of your reservation. In this case it is not as much about how long it will take as the time that the bus is departing. You will need to catch the bus at the time it is departing as the buses do not necessarily run as frequently early in the morning.
I would like to mention that another option is to take a taxi. Simply ask at the front of the resort to have a taxi called for you, or there might even be some waiting there. This way you will be able to get quickly to your reservation. The drive time should be no more than about 15 minutes, and the cost will likely be under $20. Although it is an extra cost, it might be worth the time that you save, and the extra minutes of sleep that you gain!
I hope that these thoughts are helpful for you, James. Have a wonderful time planning your vacation, and please do not hesitate to ask if you have any further questions.