Thanks for the information.
For the best prices on the fast trains, book direct with the train operator soon after tickets go on sale, usually 4 months before travel, but increasing to 6 months soon. The cost of discounted tickets keeps going up as the travel date gets closer. You can get train times and prices and make bookings at the sites linked in reply #1, using the Italian versions of town names for both sites.
From Bergamo to Firenze S. M. Novella you should book on Trenitalia, as this gives you protection if your slow Regional train from Bergamo to Milano Centrale arrives late causing you to miss your booked high speed train on to Florence. If that happens, go to the Freccia help desk on the concourse and they will transfer your booking to the next available train.