are you taking the
Disneyland Resort Express?
Here's the brochure from the Disneyland Resort Express (by Grayline)
http://graylineanaheim.com/docs/DRE Brochure.pdf
I have to say that when we were waiting for the bus for the airport, and some other small and white busses stopped by and insisted on taking us to LAX. We already had our tickets booked but I don't know, be aware that they might not be completely safe options. One of them said "Disneyland Express" in weird red letters that had nothing to do with Grayline's or DLRE logos. Pretty close, but still not the "official" service we had booked.
Then I saw a Disneyland Resort Express bus (a real one) near the time ours was supposed to arrive, I hailed and the driver pointed at another bus that was around the corner coming to our bus stop. That bus was white and large as the regular Gray Line DRE bus, but this time we didn't hesitate and took it since it had a "Disneyland Resort Express - Operated by Grayline" sign. It didn't have any other Disney images on the outside, though. Weird but it took us to the DLH and then to LAX and it all went well.
Still, we had a weird experience with the return journey to LAX. I'll tell a bit about it here in case it's useful for you or other forum members. I hope you don't mind
The driver on this "hotel-LAX" route bus hardly spoke any English and was yelling at us asking which airline we were going to take. We said "Iberia" in many different pronunciations (the american, the correct spanish, some pronunciation we made up to see if he "got" what we were saying). I even spelt it aloud for him and he kept yelling "AIRLINE! AIRLINE!" several times I had to write it down for him
, he still didn't get it and I had to reach for my airline tickets to check which terminal he had to take us to
and he asked for the tip later ... this time in cheerful manner (not polite though)...
we tipped him of course, but we weren't happy at all! we didn't pay to get yelled at! I told him this and he just smiled at me. I'm sure he understood but didn't care a bit
He also had put signs inside the bus saying "Tip... Appreciate". I can understand he expects people to tip him but I found it rude to tell guests what to do and to ask for tips when not giving a satisfactory (with satisfactory I mean at least polite) service.
that's all, sorry for the rant, but I understand it could be useful
and we made sure they picked us up 1 1/2 hours ahead of time...but talk to your shuttle driver.
They usually know the best time frame. 
