I wrote to the Hilton Rome Airport about their shuttle into Rome, they no longer offer the shuttle. They mention that the train station is close to the airport. This is what they send me.
We had not been to Rome before, so I thought it was a great way to see some of Rome sites before getting to the hotel.
I am not sure of the since it was 2019, in was mid afternoon, we walked through the airport, checked in, rested a bite, then dinner.