These recommended routes are not very long and can be done in several hours but if you choose a comfotable pace the tour will last for an afternoon or maybe even a whole day. These parts are not mountain bike tours but the differences in altitude and sometimes the bad quality of the road does require a strongly built bike.
Bicycle Tours in the Bukk are some of the best in Hungary. Bicycle route networks in the Bukk National Park were one of the first networks in the entire country.

Route 1 Blue trail on the Map
Route 2 Red trail on the Map
Route 3 Green trail on the Map