City of Rome only has 2 line of underground, which are of course not enough to reach the city in a proper capillary level.
From the B&B Savoia we have several Bus lines nearby which will bring you to the main City attractions in a very few minutes.

For your convenience, we have here a Map of the City with Public Transport lines.

note: tickets rates raised a bit recently.
updates http://atac.roma.it/