Which port are you cruising out of? It makes a difference. Generally the Princess transfers are very convenient though, but you could probably save a few bucks by making your own ground transportation arrangements.
We used the Princess transfers. I wish we had used private transportation because our flight arrived early. No Princess people were there to meet our flight and we had to stand on the street for about two hours waiting for someone to direct us. We ended up, after a long wait, calling Princess and they told us where to wait.
Had we arranged our own transportation, we could have just waited patiently at the dock without the anxiety of not knowing when or where Princess buses would arrive.
The reason there were no buses to meet our flight was because they use the same buses to debark the ship from the previous cruise that they do to pick up passengers for the new cruise that is boarding. No buses left for the San Pedro dock much before 11:00 A.M.
There is a company called "The Shuttle." They have large vans and will arrange private transportation at a reasonable cost and regular taxi cabs are also readily available. The pier is about 20-30 minutes from LAX. Some people like to fly to Long Beach airport because it is less congested and a little closer to the pier. You can find "The Shuttle" with a Google search. Just type in: Los Angeles Airport, ground transportation and shuttles. It should come up!
I hope that helps. The Star Princess is excellent, just as Harry said!