Are you the Jen of "linandjen"?
The bus is safe and for us it was fun! We rode in December and were the only tourists on the bus. The rest were workers and students commuting to and from Florence.
Have you been to Italy before? I sense a little apprehension from you and Linn. While situational awareness is a good thing, especially in the bigger cities, you need not be overly concerned.
I'm curious, it sounds like you won't have a car. While Greve is a charming town, moving about in the area without a car can be a challenge. What are your plans?
When in Greve, make sure you eat at La Cantina. Alessandro is a wonderful host. We ate there twice during our stay. You can even take cooking classes! I wish our schedule had allowed us the time to do so. Have a great trip!