https://www.flixbus.com/Has scheduled bus service from Tampa to Orlando. I think there are 3 buses a day. You can be dropped off within Uber distance of Disney. Directions on google maps will tell you how to get from airport to bus depot.
I think this is way better then Amtrack but probably not as good as hitch hiking
I think this is way better then Amtrack but probably not as good as hitch hiking