Get off at Innsbruck Hbf and take a regional train from there to Garmisch-Partenkirchen. There is one every hour during most of the day. You might change trains in Mittenwald. In Garmisch-Partenkirchen take the train on the Außerfernbahn to Reutte. Change in Reutte and go Pfronten.
Pfronten is actually about a dozen small villages that have grown together. The cluster is called Pfronten. There are three train stations in Pfronten. They are named after the village they are in, Pfronten-Steinach, Pfronten-Ried, and Pfronten-Weißbach. Reid is the main station with a waiting room; Weißbach station is little more than a bus stop with a shelter. Get off in Ried. From 6 AM to 6 PM there are regularly scheduled buses from Pfronten-Ried to Füssen. Only after 6 PM (1800) do you have to call for the AST (I found the number 1805/733773 on the RVA website). (The AST runs on a schedule - about every hour - but only if someone has arranged to be on it).
If you bite the bullet and leave Florence (Campo di Marte) at 7:50 and go directly to Verona, then Innsbruck, Garmisch, and Reutte, you won't have to take an AST. There will be a bus from Reutte to Füssen or you can go on to Pfronten-Ried and take the bus. If you wait until 11:00 and go through Bologna, you will have to call for an AST (or spend the night here, in Pfronten.) Pfronten is actually a good base to stay in while visiting Füssen. Take the 20-25 min bus to Füssen Bhf; change there to Hohenschwangau.
Look up schedules on the Bahn website. Depending on the time of day, there are alternatives. You can take a bus from Garmisch-Partenkirchen to Füssen via Oberammergau or train to Reutte and take a bus from Reutte to Füssen.