We will be in Rome in July and then have to get some transportation from the hotel to our cruise line. Is there a bus service that can pick up up from our small hotel and take us to the cruise line?
Unless you pay your cruiseline for the transfer to the ship, I think you will have to arrange for a private pick-up. You could, of course, take a taxi to Termini RR station and take the train directly to Civitavecchia, and then another taxi to the ship.
Best that you ask your hotel personnel how to get to the docks.