To get from the airport leonardo da vinci to arpinelli relais you can reach Termini Station by bus (€ 6 per person, 1 hour) or by train (14 € per person, 30 min) and from there take the 85 bus to Via del Tritone (5stops - ticket € 1.5) and walk up to Arpinelli Relais.
Or just ask me to book a private shuttle from the airport to the doorstep of Arpinelli Relais, it will cost between 60€ and 50€ (the  price depends from the time and the availability of the varius  companies, I always check for the best price),  in this case I'll need your mobile number (with national code), the  number of the flight and landing time.