do recommend renting a car... in Siena is possible!
Ciao Deb and welcome to our forum!
Would definitely recommend a car so that you have liberty to move around at your own times....
but to even see if it would be feasible to not rent a car, you'd have to see whether there is a bus from the monastery to Siena and then see timetables.... often times I've checked for others asking similar questions on the forum and it seems that there are several connections in the early mornings (between 6-8am) and in the late afternoon and one or two scattered throughout the rest of the day... might seem they are for just for commuters!
It just makes it harder to use the bus to move around (although not impossible) but you end up wasting too much time between buses and trains then I just recommend renting a car when you're not in the city itself... if you were staying in Siena city, then I would say it was doable, with just trains to catch to Florence and Pisa!