My wife and I arrived the day before departure and took the train from the airport to Tiburtina station. We purchased the tickets at the train station at the airport as well as our round trip tickets to and from the cruise port. A bargain at 20 Euros for two people! We took the local bus to a block away from the Best Western Hotel Blu. We found this non-tourist residential neighborhood to be very pleasant, with mostly locals around. There are no major tourist sights here and the locals were out and about shopping (nice little shopping mall, open on Saturday evening and Sunday, a somewhat rare find in Europe) and going out to dinner (nice selection of restaurants within walking distance). The very pleasant man at the hotel desk directed us to the mall and a good cafe for a pizza. Coffee and tea tray were provided on request. Only drawback was that all of the gelato stands had closed by the time we finished dinner and were heading back to the hotel, so have one before dinner!
The next morning we took the bus back to Tiburtina station and caught the train to Civitavecchia, changing at Trastevere station. The train was very full and when we arrived at the port we knew why - I counted no less than eight cruise ships in port, not to mention the usual large number of ferry ships.
The shuttle to the ship was pretty full but because we only travel with carry on luggage we were able to get right on the bus. The luggage compartment was full but there were plenty of seats available! So we just walked on with our luggage and put them on one of the vacant seats. Boarding went very quickly and we had time to eat, unpack and verify our dining arrangements before the lifeboat drill and departure.