We ran into this same problem when planning for our EE day on the 28th of June. We are staying at the Ramada Limited Suites Convention Center location and the hotel operator said it is 2 1/2 blocks from DL but added "they're BIG blocks." so we figured we'd be safest by planning to use ART.
I checked out their website and it looks like you can get start and stop times online in PDF version about a week before you go to the park. Outside of that, they just mention that the buses start running about 1 hour before park opening. Which doesn't help because they don't say if they are referring to general opening (8am the day we're going) or EE (7am).
So, like any vacation nazi I called them to find out details. They said that the buses will start running at 6:20 on the 28th to accommodate EE. However, this doesn't provide us with much relief because we wanted to be at the park by 6:40 or so and I don't know what stop our hotel is along the route, etc etc... We might have to call a cab afterall. By the way.. how early do people get to the park on EE days?
Anyways, the moral of the story is that ART "seems" to run early on EE days. I would check out their website and call them if you're like me and need the piece of mind.
On a side note: Does anyone know how far the Ramada Limited Anaheim Convention Center is from
Disneyland in terms of walking time or actual mileage? 2 1/2 big blocks just didn't help in determining if we could handle hoofing it there every morning...