A) FROM LEONARDO DA VINCI AIRPORT (FIUMICINO):
From the airport, you need to reach Termini station to catch the bus to the apartment. You can reach the Termini station either by the train Leonardo Express or by the private shuttle services like Terravision (http://www.terravision.eu/), Sitbus shuttle (http://www.sitbusshuttle.com/en) and TAM bus (http://www.tambus.it/). The shuttle service is cheaper when compared to the train service.
If you are taking Sitbus from the Fiumicino Airport, you don’t need to go to Termini station instead get off at Via Crescenzio (Vatican), and take the bus 32 from the Piazza Risorgimento in the direction 'Saxa Rubra' for 5 stops and get off at bus stop V.LE ANGELICO/MARESCIALLO GIARDINO.
You can get the further information regarding the transport facilities from the airport here .
B) FROM CIAMPINO AIRPORT:
There are shuttle bus services like Terravision ( http://www.terravision.eu/), Sit bus shuttle (http://www.sitbusshuttle.com/en) and TAM bus (http://www.tambus.it/) to the Termini station. It is also cheap compared to the train service. Else, you can make use of the public transit
C) FROM TERMINI STATION:
Metro: From Termini Railway Station you can take the Termini Subway direction Battistini (Line A), getting off at Ottaviano stop and take bus N. 32 direction 'Saxa Rubra' for 4 stops and get off at bus stop V.LE ANGELICO/MARESCIALLO GIARDINO.