As others have said, there is an early morning breakfast bus to the various resorts. I too believe that it starts running around 6:30 AM. You also can take a cab. There are cabs that will fit groups of 6. It will cost less than $20.
You will NOT be able to walk through Epcot prior to its official opening.
If you take a bus to DHS it is about a 20 minute, pleasant walk to the BC.
The front desk at POP will not arrange a special bus for your breakfast ADR. Often times, they don't even have good info.
Personally I budget for a few cabs for our ADR's. It just makes life easier.
Have a Great Trip.