I found this doing a google search...
Lynx is the regional bus service in Central Florida; including downtown Orlando where the bus station is located and Walt Disney World. The easiest way to find the correct route information is to call Lynx customer service; you'll need to tell them what time your train arrives and where exactly you will be heading. Disney property is huge and there are several bus stops there.
Lynx Regional Transportation Authority
Bus system
Customer Service-for bus routes and times
407-841-5969
http://www.golynx.com/?id=3
The bus service from the Amtrak station to Walt Disney World is not very convenient. It may take quite a bit of time to get to Disney by using the bus. It might be easier to rent a car; Hertz has a car rental service from the Orlando train station, or to take a taxi.
Hertz Rental Cars
Orlando Downtown Amtrak
for Amtrak customers only
https://www.hertz.com/rentacar/byr/index
Mears Transportation Company
Taxis and Shuttles
(One way ride about $45.00)
http://www.mearstransportation.com/Servi
Also check out this Mouse for Less link:
http://www.themouseforless.com/tripplanning/wdwsavings/TravelTrain.shtml