Touring Tuscany by car

I use a broker called www.autoeurope.com (company born in Germany but now based in Maine) for all my rental needs in Europe. Top service. They have deals with all major companies in Italy, such as Avis-Budget-Maggiore (Maggiore was an Italian company acquired by Avis about a decade ago and now an Avis brand), Hertz, Europcar, Entrrprise-Locauto (Locauto was an Italian company now part of Enterprise), Sixt, and so on.
Avis-Budget, Europcar, Hertz have offices in Siena, therefore you would be able to rent from those through www.autoeurope.com.
However, in your shoes, I would probably pick up the car in Rome after your visit of Rome, as you leave the city, because reaching Siena by train or bus is not as efficient as driving there from Rome (all freeway driving, so easy). If you are absolutely determined not to drive the 2.5/3 hours to Siena, then the bus from the Rome Tiburtina bus station is the better option.
Do your travel arrangements before you go to Italy. You don’t need to contact AutoEurope months in advance. I usually book my car about a month prior, but unfortunately I’ve had major family emergencies in Italy over the course of my life and sometimes had to make arrangements just for the next day. It was amazing the way AutoEurope handled my needs in those difficult times, they got me on a car at great prices just as I had to head to the airport for the first available flight from San Francisco to Italy. I could never thank them enough.

I always use autoeurope.

Thank you for the information.

You may already know this, note that each driver will require the compulsory International Driver's Permit, which is used in conjunction with your home D.L. - https://www.international.gc.ca/country-pays/italy-italie/drivers_licenses-permis_de_conduire.aspx?lang=eng . You can obtain an IDP at any CAA office for a small fee. You'll also need to be vigilant to avoid the ZTL (limited traffic) zones that exist in many cities, as each pass through one will result in hefty fines.