I can't tell you about Füssen to Reutte other than you really don't want to do that. Reutte is not that nice a town. Instead go to Pfronten, a little west of Reutte in Germany. I've made the trip by bus from Pfronten to Füssen a few times and I know it would not be too strenuous on a bike.
From Füssen to the Garmisch-Partenkirchen Bahnhof, start of the Zugspitze rail link, you have several options. There are buses (the same bus that goes to the castles at Hohenschwangau) from the Füssen Bahnhof to Garmisch-Partenkirchen via Oberammergau. These take about 2 hours. You can also go by bus to Pfronten, Reutte, or Vils and take the same train, the Ausserfernbahn, to the GaP Bahnhof.
If you take either the bus via Oberammergau to GaP, or go by bus to Pfronten and take the train to GaP, you can do the entire trip, RT, with a €28 Bayern-Ticket for up to 5 of you. I believe that with the Bayern-Ticket, you will also get a discount for the Zugspitzebahn.