Ciao cwbrick,
How is your planning going for your trip next year? I know it isn't easy, considering how travel in general is limited at the moment, but it is always possible to plan for the general parts of the trip and wait to set up specific dates once the situation has changed as regards travel and the virus.
As wbmac recommended, I would also start with the airlines. I know that it is possible to transport your bike as checked luggage but each one likely has their requirements as to how to carry it on. I know there are hard cases you can use, disassembling part of the bike so that it fits. If you search online, you'll see that these cases exist and it will just be a matter of getting the right one for your bike.
I would not consider shipping them ahead of time, other than through a courier that would guarantee the arrival in a perfect condition as they were shipped. You could look into both options and see which one is least expensive, or gives you better sense of security.
However, as Tuscany is a cycling destination, you should also look into renting a high-end road bike here. There are many companies that offer both tours as well as just rentals and they are good bikes. As far as cost goes, it might be cheaper than doing checked baggage or shipping so definitely look into it as well. Another plus to renting is you could rent road bikes for a few days, and also mountain bikes for a few more days. There are many gravel roads called "white roads" in the region and paths in the woods that are perfect for mountain biking.
As far as your base, do you anticipate doing bike rides every day? How comfortable are you with hills? Do you want to experience a mix of flat with hills? Chianti and the Val d'Orcia are very popular areas to explore with bikes, but Chianti is definitely more of a hill territory (both are but Val d'Orcia's hills are more gradual). Pretty much all the towns/villages are at the top of hills so between them means going downhill and then back uphill to the next town. If you stay in either area, you can most definitely head in a different direction every day and not get bored. I particularly love the area between Castellina and Castelnuovo Berardenga and Siena, it has a lot of hills but also a lot of vineyards and small towns and is close enough to Siena and to the Val d'Orcia to allow you to head down that way as well on longer rides. It would give you the chance to experience both.
If you prefer some flatter rides, then I would suggest staying closer to the coast, in the area near Volterra or San Gimignano. That would allow you to head east towards Chianti on some days, but also west towards the coast on other days.
You can check out
https://www.tuscanyaccommodation.com/ for places to stay at. In the countryside many farmhouses offer either apartments or rooms as a B&B (or both options) so you have lots of options. I think it is more important to decide the general area you want to stay first, then look for something appropriate. Many places welcome cyclists and have the space for storing them safely.
If you're planning to rent a car in any case, look into flying and renting out of Pisa airport, simpler than Florence.
Let us know at what point you are so that we can offer more suggestions where you need them! Have a great day!