We are going from the ship (cruise) port to Rome; we do not want to take the train; are there car services that are reasonable anyone can recommend and that we can reserve?
I'm not aware of any public bus but there is private transportation from the port to Rome. Rome Cabs is such a company. Here's the rates. Transfers to/from Civitavecchia (Rome's Port) up to 2 people, € 130 up to 4 people, € 150 up to 6 people, € 170
up to 8 people, € 200 There are 2-3 trains an hour between Civitavecchia and Rome. The fare on the IC train is 9.50E. It's even less on a Regionale train. Your choice.
Are you doing a day trip or a termination at Civit...? A free port shuttle bus will take you from your ship to the port entrance where you would meet your hired car. It is a small area so it will be very zooish finding your car and driver. Just look for a sign with your name. And if more than one ship in port have some patience.