Ciao!!
If the group coach trips for December are all booked up, then yes, the only option is to head there on your own. It isn't super difficult but it does take longer with train+bus or even 2 buses to get there. About 3-4 hours total, as opposed to about 2 hours by car.
You can take train from
Florence to Pistoia and then from Pistoia take bus #54 to
Abetone.
You can check train schedules on Trenitalia here:
https://www.trenitalia.com/it.html
You will have to go to the AT Bus website and download the PDF file with the timetable here:
https://www.at-bus.it/it/linee-e-orari/pistoia-extraurbano-54
To make it a whole day trip, you'll need to be in Pistoia to catch either the 6.41am bus or the 8.11am bus (gets to Abetone by 8.30am and 10am, respectively) on weekdays and Saturday - don't try to go on a Sunday as the hours are more limited.
The last buses from Abetone are at 5.15pm and 7.15pm, and take about 2 hours to get back to Pistoia.
Hope this is useful, let me know if I can offer any more assistance.
Editing to add: not sure if it's really an option because not sure of cost, but you could theoretically take a taxi from Pistoia to Abetone rather than the bus, it would cut the time for sure.
Or rent a car for the day?