I'm sure some roman monster driver will come and help you with local info.
Meanwhile I found a couple of bike rent company offering also Ducati bikes:
http://www.cimt.it/motonoleggio.htm (MTS1000, ST3)
http://www.happyrent.com/listino/listino.htm (Monster750, ST2)
Hope this can help. For any questions, please do not hesitate to ask!
Enjoy your roman stay!!