I would call Mears (1-800-759-5219)
When we arrived at 12:30 by the time we picked up
our bags and walked to their area,It was downstairs and to the back of airport ( not hard to get to) they were loading a bus (small Van Type) for Disney.. I was suprised at how many
people were arriveing at that time..Anyway, I called before We left home about a day before.Just incase I had to get a taxi They said a shuttle would be available as they were picking up
passengers from Disney.. Does this help..By the way we left Disney at 11:00 pm and had no problem getting a shuttle from Mears.. If you are concerned try Tiffiny Town cars.. They run a private car out to you ( 1-888-838-2161) they also
run to Disney ..Their service is quite good, a bit
pricy about $ $75.00 but don't quote me there..
I use mears mostly because they have a contract with one of the company's we deal with not that I get a discout but they only charge 40,00 so I can handle that I tend to be cheap in the transportaion department..My motto is just get me there and back don't need much more.. So if you are worried Call..Have a good one.