The nearest station to my B&B will be the San Pietro station on the Roma-Cesano line.
On the metro map its listed as FM3.
Does anyone know if this is included on the Roma pass? Roma Piu pass?

It's included in the plain Roma Pass. If you go to www.atac.roma.it and look for the map of train and Metro lines, everything is included up to the stations whose names are printed in red.

Yes, that's the Rome-Viterbo line and is included in the regular Roma Pass. See map here:
http://www.atac.roma.it/docunet/file.asp?mid=3&rid=385

Roma Pass Transport
Free admission to ATAC urban buses and trans, Underground lines A and B, Met.Ro trains: Roma - Lido, Roma - Viterbo (in the Roma - Sacrofano section), Roma - Pantano railways lines.

Roma&Più Pass Transport
Free admissionto ATAC urban buses and trans, Underground lines A and B, Met.Ro trains, extra-urban coaches Cotral and regional railways Trenitalia - 2nd class (except special connections, Leonardo Express and local urban services though carried out by Cotral).

What is the Piu pass, gives you free rides on some transport to the suburbs?

Where and when is the best time to get one of these week passes?

Can you buy on a bus? If you're staying mostly around Campo de'Fiori, can the metro be of much use?

I stayed near the Spanish Steps once and went to the metro station there to buy a 3-day pass I think. But only used the metro to go to the Vatican museums mostly and a couple of bus rides.

Many of the bus signs don't really give you a sense of where a particular bus is headed.

scrb, The Roma & Piu pass gives you free transport to places in the province of Rome not covered by the plain Roma Pass. Both give you free access to two museums or archeological sites and discounts to others as well as free transport.

For information about buying either pass, see www.romapass.com.

They are not weekly passes; they are valid for three days.

It's true the Metro does not give much access to the historic center, but I do not agree that the bus signs don't really give you a sense of where a particular bus is headed: Every bus sign lists the stops on the bus's route.

Thanks Zerlina.

I haven't plotted my itinerary yet. It will only be worth it if I go to places like Galleria Borghese again.

Otherwise, I would look for a transport-only pass, without the 2 free museum entries.