I'm a little bit confused. Are you talking about transportation to ONT at the end of your cruise or transportation from ONT before your cruise? Either way, I don't think there is scheduled shuttle in either direction. If you booked your flights through Princess, they might have a shuttle going to the Port and then back to the airport after the cruise. Princess should be able to tell you that.
I'm assuming (which might be a mistake) you are sailing the Mexican Riviera. If you are, I hope you have a terrific cruise. We have done that itinerary many times. Anymore, we don't even get off the ship because we have been to the ports so often. For us, the ship is the destination.
Ray