Get in touch with Gianfranco (owner of B&B) before your departure from your country/place. Ideally request him to arrange your cab for pickup from FCO Airport to the B&B. So that he can be there to help you get into the Apartment as well as provide you with valuable information about Rome and how to get around there. We followed his guidelines and directions as much as possible and we had a good time in Rome. Gianfranco is a people's person. Carry your shampoos with you, if not ask for the same. If you ask Gianfranco would do as much as possible by him.
The B&B is very close to Cipro Metro train station on Line-A. It is about 10 mins walk to Vatican Museum Entry.
If you want to get to Colosseo, then take Line-A from Cipro towards Termini and change there for Line-B towards Colosseo. Travel wise, any kid under 10 years, can go free on Metro.
The coffee at B&B is awesome, nice Espresso. You get good continental breakfast like Croissants etc.,
When you get to Colosseo, you can plan to visit: (Excuse some spelling mistakes as I'm not Italian)
1) Ofcourse Colosseum
2) San Clemente (This is lovely, Church is built on top of 2nd century Church, which is in turn built on 1st century Church). 5 Euro entry for Adult. Children under 10 go free. As soon as you get out of Colosseo, turn left and walk straight ahead towards traffic lights and it is further 400m or so.
3) Right opposite to Colosseo and across Colosseo is the Palatine Hill and Roman Forum.