It's run by GrayLine. There are buses every 30 minutes from LAX to
Disneyland.
We are going in 3 weeks and I just called them this week to see about reservations.
You do not need a reservation. You just show up at their stop outside baggage claim in each terminal.
The first stop is the Disneyland Hotel. There, an agent gets on board and collects payment from everyone who is not prepaid, finds out where everyone is going and then routes the bus to its next stops based on who is on board.
You can reserve online and prepay. I wanted to use a
AAA discount, which you cannot do on line. My only option is to pay on board the bus. You can purchase one way or round trip tickets right there on the bus.
You can read all about them here:
http://www.graylineanaheim.com/airport_info.shtml
They do recommend a reservation for your return trip to LAX- but you only have to call 1-2 days ahead from your hotel.