On each ride, with different bikes, my rides are automatically assigned to "road cycling."
I am also annoyed by the lack of this feature on the Fenix watches... I also have an Edge 520 and that lets me to select a different bike profile for each ride. I took a look at the FIT file specification and the SDK and the difference boils down to the Edge sends the name of the bike you've selected as the name of the "Sport" - the Fenix just sends the generic string "Bike".
Edge:
Sport Name: Stache <-- matches the name of a bike profile in GC
Sport: CYCLING
SubSport: MOUNTAIN
Fenix:
Sport Name: Bike
Sport: CYCLING
SubSport: MOUNTAIN