Bologna/Modena Sept 24

Assuming you are taking the train
Florence to Modena -change in Bologna -visit Modena before lunch
Then
Modena to Bologna after lunch to visit Bologna
Train Bologna to Florence

Trenitalia

https://www.trenitalia.com/en.html

Firenze SM Novella
Bologna Centrale

No real need to purchase in advance, there are frequent trains

Thank you! Anything specific we should see in the short time we have? Was thinking of a tour of some sort... balsamic or parm? Probably cliche so if there is anything else, I'm all ears :)

I suppose you could do a morning tour in Modena

I HIGHLY recommend the Italian Days tour that departs from Bologna, but it's a long full day. If there is any way you could make it work, you will not be sorry.

I think there's a couple of acetaias in Modena city center that do tastings. Proscuitto/parm production facilities tend to be away from people because they stink and need a lot of space, but you could find some at the Albinelli market (make sure it says DOP).

If you're doing a la carte at Osteria Francescana, make sure to get the 5 ages of parmigiano. It comes and goes from the tasting menu, but I think it's always an a la carte option.

Probably the best solution for you is hire a driver from Florence and along the way to Modena you can do a stop to visit a Parmigiano-Reggiano dairy. The tricky part is that the best moment is at early morning (when they are working), arriving not after the 9am, After the visit and tasting you can move to the center of Modena for lunch.
Lunch should finish at 4pm, so not too much time for visits after that. The best could be a walking tour of Modena, like the cathedral and the most important monuments, before being driven back to Florence.
Bologna is really difficult to be fit in a day like that. For one reason because there is a lot to be visited and secondary because the traffic to reach the center is often very bad and make you waste a lot of time.

There aren't regular group tours who can fit you schedule, but Emilia Romagna Tours is a local operator who can arrange a private tour for you.

I suggest visiting Modena instead of Bologna since you have limited time.

If you want something really special, you could see if tickets are still available for the Sept 26 performance of Otello at the Parma Festival Verdi. Opera in Parma is a very big deal.

Ferrari museum in Modena.