According to the Celebrity app "A complimentary shuttle bus will be available from the ship to the center of Livorno. Complimentary round trip tickets will be provided by the Port Staff at the pier. Please collect and keep the tick with you for your return to the port. The first shuttle will depart upon arrival to the port. For your convenience, shuttle buses will run continuously throughout the day. Last shuttle to the ship is scheduled for 11pm and resumes the next day at 7:30 am."
You should definitely confirm the times when there.
