What time of year are you visiting? That can make a huge difference.
We generally visit at times of "moderate" crowds (4-7 on the touringplans 10-pt scale). We aim to arrive at our park of choice about 45 minutes before it opens (keeping in mind that there are often several "rope drops," one occurring before the scheduled opening after which guests are held at a central point, and then others throughout the various "lands" that occur simultaneously closer to opening time), and we plan on waiting for a bus for up to 15 minutes. Depending on whether we get a bus right away, or have to wait awhile, this typically puts us anywhere from first in line to 100th in line at a set of tapstiles. (Either way, we're among the first to reach our desired attraction.) If you were visiting during a time with higher crowds, you'd want to show up even earlier.
So, to do the math: for MK from WL (~10 min. trip) - be at the bus depot 70 min. before the MK's scheduled opening (add a few extra minutes if taking the ferry boat, as they don't come as frequently as the buses in our experience).
For Epcot (~20 min. trip) - be at the bus depot at least 80 min. before scheduled park opening.
For HS or AK (~30 min. trip) - be at the bus depot at least 90 min. before scheduled park opening.
All this being said, due to transportation delays we've also arrived just as a park opened -- breezing in on the heels of the rope drop crowd -- and have enjoyed all the same advantages. This was even true on our last visit, when the kids and I waltzed into MK at around 8:50am (9am opening, but gates opened no later than 8:45am) on the Monday of Thanksgiving week (a crazy-crowded time to visit), and hit half a dozen headliners in 2 hours with virtually no wait. As a responder below said, the most important thing is to be there at rope drop, regardless of whether you're among the first in line.
Good luck, and may the caffeine be with you!
