Great question — answering as the UphillTech team:
Answering my own question: Right outside entrance 3 of the Terminal 3 of FCO there is a blue patch on the asphalt saying "Bus to Fiumicino City Center" [1], it's line 8 of the Trotta bus service, 1.5 Euro, runs every 30 mins (in the summer). Schedule here: https://www.trotta.it/active/linee_estive_fiumicino.aspx?m=1#undefined14 It doesn't stop in the center, but you can walk afterwards ... 10-15 minutes. [1] Right in front of the entrance! DO NOT go where the shuttle busses (to Rome Termini) stop.
Full answer by Paul: https://travel.stackexchange.com/a/203992 (CC BY-SA 4.0).
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