It's a long ride from Civitevecchia to Rome. Traffic varies a lot and can be very heavy. Count on definitely 1 hour plus and it is perfectly safe for a couple to go on HAL's bus to Rome. Spend a wonderful day on your own and have the peace of mind to know your transportation back to the ship is HAL's and the ship will wait for you if you are delayed. If you go on your own, you have to worry more about returning on time.
Plan your day in advance to make the best use of your time.
Seeing we were six people and we wanted to show them as much as we could, we decided to ride taxis between tourist areas. I rode with two others in one taxi and my husband rode in the other. Rome taxis are tiny. We know our away around the huge City of Rome but our friends had never been to Europe. We could see they were uneasy about one couple or the other being alone in the taxi.
I don't recall the order but what they wanted to do and see was:
St. Peter's Basillica
A bit of shopping on Via Condotti
And especially a fabulous lunch at our favorite (at the time) Trattoria.
That is a lot to do in one day but we managed to move right along. They were content with a quick visit to St. Peter's. We have spent many, many hours there and still have not seen it all so you have to decide your priorities.
With only one day, a quick overview of as much as possible is wonderful fun IMO
Use the normal common sense when traveling around Rome. Like most European cities, there are gypsies who are adept pickpockets, ladies wear your purse cross body and have as little as possible in it. Keep some folded paper money in a shoe, just in case. Gents.... don't put your wallet in your back pocket. Pay attention to your surroundings. They almost never want to injure tourists and are only after your valuables. Don't let yourself be an easy target.
Ladies....... put a credit card in a 'safe place'
, just in case.