The bus service is called Disneyland Express but it usually takes longer than Supershuttle because it goes to Disneyland Hotel first, collects fares there and then puts people on busses or shuttles to their actual hotel. Sometimes you stay on the same bus. Same for the return, everyone goes to DLH. The time I used it from PP, I did have to change busses. It's not operated by Disney, it's operated by Gray Line.
I have flown into both LAX and SNA. If I can get a non-stop for the times I want and the fare, I will fly into LAX (no non-stops to SNA from PIT). If there are no non-stops to either, then I will go with SNA.