We've used Disneyland Resort Express in the past, several times. I'm hesitant to go with them any longer, though, unless I pre-pay. They tend to "forget" their prices, and attempt to charge some people more than others. Quite honestly, we weren't impressed that DH and I were $12 more expensive than the family of 4 sitting in front of us! (And I made a big stink, pulled up their website with prices, and everyone else on the bus was then well aware of what they should be paying.) They are currently $48 per person, roundtrip, and up to 3 kids are free per paying adult, so you'd be looking at about $200 for your group. With this option, you can pre-pay through their website, I believe (I have done it in the past, but it's been like 18 months), so no one other than headquarters ever has your card number.
Without discounts, renting an economy car for your whole trip from Alamo is under $220. (Keep in mind, though, you may need to pay parking fees at your hotel.) Or, again with no discounts, from LAX to Downtown Disney is $99 through Alamo, and $51 to get back. These are prices without taxes included. Alamo is a well-known business, so your card is safe with them. Their drop-off and pick-up locations are right there in Downtown Disney, too, which is sooo nice! (Thinking of doing this myself for my trip in February.)
I believe Uber is also an option, though I can't check the fares at the moment (page isn't loading right on my computer). You pay through the online (secure) site, and the Uber driver never has any contact information. I believe Uber has a heck of a discount code available online, too... like $30 off or something?!