Thanks to traveller named Bob for this advice:
Option 1 is to do a 2 bus trip by going from La Fortuna directly to San José and from there on to Puerto Viejo, but we were told there is not much time in San José, and as you can read on this page the second bus does regularly sell out. So for us this sounded a bit risky, so this is what we did:
Option 2 is to take the bus from La Fortuna to Quesada (via El Tanque, this should be the fastest), check the La Fortuna page for a photo of the schedule. We took it at 8:00am and arrived at 9:20 in Quesada. It costs 2800C.
Next bus is Quesada – San José, 10:00 – 13:05 for 1800C. The boletería in Quesada opened around 9:45 (so 15 mins before the bus left), and there was already a queue before that time. Join it while your waiting anyway!
In San José you have to switch to the MEPE terminal, which is a less than 5 minute walk.
Our last bus was as described in this page (Thanks!): San José – Puerto Viejo, 14:00 – 18:45 for 5590C. There was a bathroom/snack stop of 10-15 minutes at the bus terminal of Limon around 17:15.
For the early risers: we got advised option 2, but starting at 6am. This should allow you to catch the 12:00 bus in San José and reach Puerto Viejo in daylight.