Not a long walk at all - the bus depot is maybe a hundred yards from the park gates, although the bus may drop you off in slot that might add another 50 yards or so to the walk.
A cab would get you no closer - in that case, your best bet would be to be dropped at the Contemporary (leaving you a walk of perhaps a quarter mile, or a little less), or at the TTC or the Grand Floridian, where you could catch the monorail.
One thing that is pretty widely agreed on is that for the MK, Disney transport is probably the best way to get there. (That may not be the case for the other parks, where there's no lake between the parking area and the front gate.)