There are a lot of conversations on here about this about people arriving earlier and no solutions were ever given to would accommodate anything as late as 3 (and who knows how long luggage/customs might take). I'm always personally paying attention since I'm often in that predicament.
My recommendation (is what I usually do) is book a shuttle pack with Montezuma Expeditions (I'm sure some other companies do this too). That includes cab from the airport to an inexpensive hotel in Alajuela and a shuttle will pick you up early (6 or 7 usually) in the morning and take you to your hotel in Montezuma (noon or 1). It's around $80 but that's cab, shuttle, ferry and usually breakfast (if your shuttle is before breakfast, talk to them, they'll open a few minutes early or make you a something to go, sometimes small, sometimes awesome). FYI, the shuttle does not usually board the ferry so you carry your luggage on the ferry and catch another shuttle on the other side.
I always ask for Casa Tago on the shuttle pack, they stuck me there once when the other places were full, and I pay extra if it's not on their list of options and pay extra bucks for A/C (so about $90 total with my extras). Yes, it's more than $50 but it's also a night of hotel...
You could pay for a hotel (?$), cab it to San Jose ($25) to catch the 6am directo bus for $14 (which has a locked, ticketed luggage carrier and A/C). But you're probably higher than the shuttle pack fee at this point (and your traveled 25 minutes east and now you have to travel it back to go west). The big bonus of this is the luggage stays locked under the bus.
I've never taken the regular public bus (the NON-directo) to Puntarenas, I've always been confused if it takes you to the end of town (end of peninsula) where the ferry is or if you have to take a cab (I think this is the case). And people always say to worry about your luggage.