There's a bus every 5 minutes or so, which will get you in the hearth of the Histotical Center of Rome in 5 minutes.
As usual, get standard tickets in advance at tobaco shop or news paper stands, or get a Roma Pass.
Most of time, just get a 75 minutes (1,5 Euro ticket) per way and you'll be allright.
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Legenda
Orange: B&B Savoia
A: American Ambassade
B: Tritone Fountain
C: Spanish Steps
D: Trevi Fountain
E: Pantheon
F: Navona Square
G: Trajan's Market
H: Foro Romano
I: Colosseo
J: Campo de' Fiori
Red Polygon: Trastevere Neighbourhood (nice at night)