Okay my dear lady, I've been working on this for you. Here's what I've got...
You should try and stick with a
scheduled/reserved shuttle bus service, because LAX recently forced all Uber/Lyft and Taxis off the airport roadways. You now have to take a shuttle bus to the off-property Uber/Taxi lot and then find your car there. And it's been a NIGHTMARE. The process is not smooth and it wastes a lot of time getting to and from the satellite lot, and then when you get there it's a giant parking lot with multiple islands clogged with crowds and traffic and everyone hates it. It's been in the local media a lot here lately, but those outside of SoCal probably haven't heard about it. As if LAX needed more headaches and bad press, but they managed to pull it off and make it worse!
They call this process "
LAX-it". Seriously. Get it? Like Brexit? Except you are trying to exit from LAX, but they won't let you.
So, whatever you do, try and aim for a dedicated Disneyland shuttle service as those buses are still allowed to pick you up at the airport itself right outside baggage claims, noted by the orange loading zones for "Shared Ride Vans/Charter Buses".
Here is the most successful one that serves LAX and Disneyland area hotels...
dre.coachusa.com
On a recent overseas trip, I used them by taking a Lyft from my house to the Disneyland Hotel and then boarding the Disneyland Express to LAX a half hour later. You tell the bus driver which airline you are on and he drops you off right in front, and pickups are done right outside all baggage claim zones. The trip in early afternoon took me about an hour from the Disneyland Hotel to the Bradly International Terminal. The bus was clean and modern and the service was fine, although the bus driver got on the PA and tried to start impressing the tourists with a silly Hollywood patter as we got closer to the airport in an attempt to boost his tips.
I only gave him a Fiver for helping with my bags, when if he had just stayed quiet and professional I would have given him at least a 10. But for LAX nowadays, if you aren't renting a car, a reservation on a dedicated bus like Coach USA's
Disneyland Express is your best bet. Just avoid taxis and Ubers because that process has devolved into anarchy and endless delays at LAX!