Disneyland Resort Express was operated by Coach USA but shut down three years ago. They were directly working with Disneyland and were authorized to use their trademarks.
There is one company operating as "Disneyland Express Shuttle" but I'm a little bit skeptical that they have authorization to use that name.
Disneyland has its own recommendations. They mention public transportation, but some have indicated that some of these routes go through iffy neighborhoods, even if it's on a light rail vehicle. The only shuttle service they list is Karmel. They also mention Lyft but not Uber.
https://disneyland.disney.go.com/guest-services/getting-here/by-plane/
I did a sample for Karmel Shuttle from LAX to the Disneyland Hotel, and it was saying 1 to 5 passengers was $126.50. But if you've got less than 5 passengers it can still be a shared ride and your party costs the same. Doesn't make sense to me. I picked a random time for tomorrow afternoon, so who knows.
Whether you have 1 person or 5 people in your party, the rate is the same. This is a shared ride service. You may SHARE the ride with other passengers. You may be sent a Shuttle Van/Bus, SUV, Sedan or Compact SUV. Shared ride is only available for pick-ups between 6:00am and 7:00pm. Private service is available 24/7.
I'm adventurous (i.e. crazy) enough to risk my personal safety on public transportation in LA County. I already have the fare card, and I believe it would cost $1.75 plus the fare card to take the airport shuttle, LA Metro Green Line to Norwalk, and then the LA Metro 460 bus to Disneyland. But then again I can deal with the homeless, mentally ill, and just plain belligerents I've seen. You may not want to.
If it was Orange County Airport, I was thinking maybe the new EVE service. Would be interesting if maybe LA Metro might be interested in something similar from LAX, although I'm not sure they would be able to use anything other than Metro's existing bus stops.