Although biking in the park itself is prohibited, the mountainsides around Parque Nacional La Tigra [1], especially in the vicinity of El Hatillo and farther north, are crisscrossed with hundreds of trails and dirt roads suitable for mountain bikers. One local rider declared, his eyes shining in quasi-religious rapture, that the region around Tegucigalpa [2] “es un paraíso” (it’s a paradise) for mountain biking.
Amitigra (tel. 504/238-6269, www.amitigra.com [3]) can provide information about routes; some are outlined (in Spanish) on their website (look under Ecotourism/Actividades/Ciclismo).
Amitigra can also help organize rappelling for a mere US$12 a day, not including food or transport.
Links:
[1] http://www.moon.com/destinations/honduras/southern-honduras/near-tegucigalpa/parque-nacional-la-tigra
[2] http://www.moon.com/destinations/honduras/southern-honduras/tegucigalpa
[3] http://www.amitigra.com