I contacted a limo service I found on the internet. They had a driver with a small van meet us at the dock. He had a sign with our name and I found him with no porblem. Cost was 100 euros total for four people with two large suitcases each little less than the Cruise ship transfer, but We did not have to ride on a bus so it was worth it.
IF I had to do it over I would fly to Italy, take the Express train into Rome, and take train to port. Keep in mind train arrives in Rome on one side of station and you have to walk to the other side to of the station to get the train to the port. Once your at the port train station its a short walk from the station to the port bus shuttle stop. Port shuttle bs is free to your ship.
On return I would take train from port to Rome, stay a few days in Rome and then take express train to Airport.