The Disneyland Resort Express is a service run by Grayline. There are fairly strict hours, so look thoroughly at their hours-of-service information, maybe even call them, to make SURE you can get on it if you're leaving late.
A shuttle, like Super Shuttle or Karmel Shuttle, might be better, for more personal service.
BUT if you're going to an airport hotel up near LAX, rather than going to the airport and then calling the hotel and catching their shuttle, it might save time and hassle and get you to the airport quicker which gets you more sleep which makes the next part of your journey nicer, if you find a way that takes you hotel door to HOTEL door (and that is NOT going to be the Express bus, and might be more expensive than taking the *airport* shuttle services). I'm pretty sure that a place like Super or Karmel Shuttle could accomodate it, but it might be a bit more costly, so...get the information and figure out what's in the money and time budget!