Bus from Monteverde to Liberia, Costa Rica

Indeed, that is a solution recommended by the hostel "Casa Tranquilo". There is this intersection called "La Irma", named after the gas station at the crossing of route 1 (between Puntarenas and Liberia) and route 145 (leading to Tilaran).

As written in the timetables linked by the hostel and the one from the tourism board @pnuts found, there are buses between Puntarenas and Liberia stopping at this intersection. It is hard to predict the time it will come, though.

Based on these, the bus takes 3 hours to link Puntarenas and Liberia and the earliest leaves at 5AM, so I suppose you can expect it to pass the intersection between 6 and 7 AM (and the second one will come 30 minutes later). Given that your bus from Monteverde left at 4.20 AM and that, according to these bus times, it takes 3 hours to link Monteverde and Puntarenas, I guess you will arrive at the intersection between 5.30 and 6.30 AM. So you will probably not wait too long there (I'd guess at most 1 hour), depending when the buses pass.

There are other options, according to the timetable from the tourism board. You can go to Tilaran, which takes 2h30 and the first bus leaves at 4.30AM. From there, you can take a bus to Cañas at 8 or 9 AM, arriving there 30 minutes later. It will take you 2 other hours to reach Liberia, leaving at 8.30 or 9.40 AM.