Many Canberra nature reserves have been reviewed on Australian Hiker.
Cycling is permitted in 30 of the Canberra Nature Park reserves. Information from the Management Plan 2019 can be found in OpenStreetMap. The rideable reserves are previewed here.
Throsby, Gungahlin, has an excellent bike path and views of the Goorooyarroo Nature Reserve.
There is a long list of missing links: route and tracks that could be opened for recreational biking. We can thank the Canberra Centennial Trial for opening a lot of the ACT commonwealth land for recreational use.