Public transportation from Bologna to Florence

Bus 40 from the airport to the Bologna Central Train Station then train to Florence.

There are also some direct buses departing throughout the day. The airport webiste has information and links - scroll down to Travel to/from and click on bus.

The cheapest option and probably the most convenient (if the times work for you) is the direct shuttle bus to Florence (90 min journey).
https://www.appenninoshuttle.it/?lingua=2

Another option is either a taxi or the Aerobus to the Bologna Centrale train station (25-30 min depending on traffic)
https://aerobus.bo.it/en
Once at the station you’d take one of the frequent fast trains to Florence (35 min) for 29€ one way.
https://www.trenitalia.com/en.html

If you travel after November, there will be the new Marconi Express fast people Mover from the airport to the Bologna Centrale station which can take you there in 7 min. The new people Mover was scheduled to open this month but the inauguration was postponed a month for some additional tests.