According to the ART website if you are staying at the Double Tree on Harbor near Orangewood Ave. then it has its own ART stop on route #3. ART usually begin operations 1:40 before regular park opening so if you catch the first bus you should have no problem making MM.
Taxi worked for us a couple yrs ago when we stayed on that side of town. We called it a bit earlier and it was prompt. It was for an 8am opening (not MM) and we were concerned about rush hour traffic since it was middle-of-the-week, but it wasn't a big deal. About $15. ART is def cheaper and since it isn't the most reliable bus system in the world, I second the idea of being there (at the stop) for first pick-up.
There is an ART route that goes to the Block at Orange and Crystal Catherdral. It doesn't run as frequent as the other ART routes so I doubt it will work to get you to MM.
There is an OCTA bus stop across the street in front of the Ayres Inn that goes down Chapman and you could transfer to one up Harbor.
Just so you know the Catholic Diocese of Orange recently bought the Crystal Cathedral. They will be converting it into a Carholic church and have renamed it Christ Cathedral. So if you hear the term "Christ Cathedral" keep in mind that they are also referring to the former Crystal Cathedral.
I'll look into ART, I think the stop is by Krispy Kreme at the Block at Orange. If not, I might just drive to Dland that day. Parking costs the same as a taxi!
Twice as much unless you plan to never leave DL!
Anyway, if you are planning to drive, take the Toy Story lot. from your hotel it is a very quick drive down Chapman and a right on Harbor and a right into the lot. The difference to us in how the traffic flowed in the morning was like night and day. I dunno if I'll ever park in M&F again! I can't say enough good things about it and I know there are others that think I am crazy and that there is no diff at all (one of those ppl were in my party!)
A little off-topic, but all this talk of busses and shuttles brought to mind the old spiel, "...this tram goes to all sections of the parking lot, except for (I forget -- was it Bambi and Cinderella?)...it does not go to the Disneyland Hotel, or to the Orange County or RTD bus stops..."