It´s not possible to cycle up to the top of Chirripó but it´s a magnificent hike. After leaving Montezuma and the Nicoya, I left my bicycle with couchsurfing.com friends in Puntarenas (thanks to Alex and Mel and their families).
Although a long hike, one of the hardest parts of Chirripó was probably getting the passes to stay at the huts at Base Crestones (6 kms from the summit and 14km from the start). Audie and I had to camp outside the rangers office for the night from 10pm to get them since only 10 spaces (maximum) for those who show up without booking ahead (hard too). The alternative is to do an overnight hike for which I heard times varying from 10 to 20 hours. Beautiful terrain either way. I ended up staying three nights instead of the two that I´d booked after pleading with the ranger. There seemed to be space in the hut even though people were told it was fully booked at the bottom. Absurd, presumably the spaces are reserved by companies doing tours and unused sometimes if they don´t fill them. A flawed system but if you really want it you can get to the top one way or another, and it´s worth it.