There are both- shuttles and a bus.
The bus is the
Disneyland express bus. From what I understand, it is not as complete of service as the magical express at WDW. It does get you from the airport to the hotel, but they do not handle your bags for you. You'll have to claim your bags at the airport and get them to the bus. Then they take them off for you at the hotel and you get them to your room.
There are buses that service LAX and SNA airports. You can find out rate info at
www.airportbus.com. You will also find a brochure, in pdf format, that has times and estimate trips times on it. The service is actually contracted with Greyline (Grayline?). You can use them for other transportation as well, such as to seawork or universal studios.
A lot of people like the bus service. Its not my favorite way to get around. The bus is large and holds a lot of people. Depending on your hotel, you may be on the bus for a long time waiting to get dropped off. Then on the way back you have to ride the bus to the Disneyland hotel, and switch buses depending on what airport you are going to. Just is a bit more hastle then I like. The bus will run you about $15 per person each way. There are often coupons on the website I gave earlier. Probably a good options for LAX, not as great from SNA because its so close.
There is also supershuttle and a couple other shuttle companies. You may share your shuttle with other people. So it is possible that you may have to go into residential areas to drop off. That has not been my experience, but I've read that other people have had to. We've always just dropped off at other hotels, and never more then 2 besides our own. They have always been quick and easy to use. Get pricing at
www.supershuttle.com
They service LAX, SNA and Long Beach (probably Ontario and Burbank as well)