is this special bus in rome covered by the BIG ticket or is there a separate fare?

The 116 (a small bus that I've taken between the Via Veneto area and the Campo de Fiori area) is covered.

Do you mean the 110, which is the hop on hop off bus? That is not; the cost is 13 Euro.

Thank you. I was hoping to take the bus #116 from St. Peter's Square to Piazza Navona, Pantheon, and Trevi Fountain in one day. Seems like it is possible on this bus route.

I think it does, more or less. It starts from somewhere called "Terminal Gianicolo," which seems to be near but not on St. Peter's Square.

You can go to

www.atac.roma.it

and enter "116" into the box under the words "Trova Linea" in red. There seem to be five variations of it, but I was unable to discover what they were exactly. (You'll get what looks like a white page; you have to scroll down and a map slowly appears.)