I don't know much about bonsai trees, but I was quite happy to find this place, a garden in Via Cecconi, open on a very hot Sunday August morning. The mature trees are neatly arranged in display pots, some also have fruits.
In a nursery of sorts the younger plants are kept in temporary pots. Here is Gian Carlo, my guide for this visit.
External links:
Bonsai (Wikipedia)