It is a 15 minute drive without traffic; however, with traffic it can take 45 minutes, but chances are closer to 20-30 minutes, depending on time of day.
Most Cabs offer flat rates to
Disneyland from LGB, just make sure you ask for it, otherwise it is expensive. Depending on your party size, you might want to talk with others on your flight to see if they would like to share one of the larger Van taxis, as the flat rate is for all people, not per person. By doing this, it might be cheaper than a shuttle, of course depending on the number of people, it might be cheaper to take a Taxi anyway.
However, due to how few flights come in, Shuttle will usually be scheduled to leave shortly after a flight comes in.
I do have a warning though, once you fly into Long Beach, you may never want to fly into a different airport again, as you will find it is a very convient airport, especially when leaving and going through security (usually takes about 5 minutes or so), you only ned to show up at the designated time to give the airport time to load your luggage onto the plane.