If you are relying on public transportation in the Zancudo / Pavones area, you will have very few options. There are private taxis that will take you just about anywhere but all rides are very expensive. Taxis average $50 USD to go between Golfito or Paso Canoas and Zancudo.
The big pink, green, or orange Tracopa buses will get you into the general area, there's a boat between Golfito and Zancudo, a few public buses that run in the area, and some shared taxis to get you between those buses and Paso Canoas.
I have created a very rudimentary map to give you the lay of the land and the current bus routes.Transportes Barrantes Facebook page shows (most of) the times for the buses around that area but it's missing the Langostino to Neily at 1 pm. Check their home page too for special schedules.
Transportes Barrantes Schedule at time of writing:
Punta Banco-Golfito 5:30 a.m.
Pavones-Golfito 12:30 p.m.
Golfito-Pavones 10:00am y 3:00p.m.
La Esperanza-Ciudad Neily 5:15 a.m.
Zancudo-Ciudad Neily 5:30 a.m.
Ciudad Neily-Langostino 9:30 a.m.
Ciudad Neily-Zancudo 2:15 p.m.
Langostino-Ciudad Neily 1:00 p.m.
The times I'm most unclear on are when the Neily buses actually come through Laurel and Comte on their way to Zancudo, Pavones, or Langostino. That's key because if you are in Paso Canoas (a popular stop), you will need to time your shared taxi to when the bus comes through. For the Neily - Zancudo bus, it's something like the bus that leaves Neily at 2:15 pm, hits Laurel around 3pm (or is it 4pm??) and gets into Zancudo around 5:30pm+. I do see the bus coming into town at around 5:35pm each evening.
Paso CanoasPaos Conoas is a popular town for either passing through on your way in and out of this area or for going shopping. There's a free zone (you don't have to go through immigration) in Panama with tons of departments stores and liquor stores and is a good place to stock up on things that may not be dirt cheap, but they're cheaper than Costa Rica.
To get to and from Paso Canoas and the beach towns, you use a shared collectivo taxi to shuttle you between Paso Canoas and the bus stop towns of either Laurel or Comte. Either town is fine, it's just a matter of spending more or less time/money on the slow bus that will take you to the beach (Laurel is further from the beach towns but closer to Paso Canoas).
A shared taxi between Paso Canoas and Laurel should cost ₡1,000 (about $1.75) and takes about half an hour. If coming from Paos Canoas, you'll then get the Neily bus as it comes through at 3 pm on its way to Zancudo for around ₡1,600. The ride takes at least an hour and the bus will drop you off anywhere on the road that you ask. A collectivo between Paso Canoas and Comte costs ₡2,500 (45 min.).
You can find the collectivo taxis in Laurel and Comte waiting where the bus stops. In Paso Canoas, you'll see tons of them near the border. The taxis will be more than willing to take you in a private taxi (for something like $30 USD!) so make sure you specify collectivo. Hopefully there is anther person going the same way so you’ll share the ride with them (I don’t think the taxi will go if there’s only one person) and your driver will try to pick up additional people along the way.
ZancudoLike Pavones, there are limited bus options. There's one bus per day that leaves Zancudo at 5am, goes to Ciudad Neily by way of Comte and Laurel, and returns in the evening. There are a few other straggler routes in neighboring towns (for instance you'd have to get someone to drive you to Langostino to get the bus from there), but that Zancudo - Neily bus is your go-to. But Zancudo has the added bonus of the boat to and from Golfito.
The public bus between Golfito and Rio Claro costs about $1 (1/2 hour). You pay the driver when you get on. If going to Golfito, ask him to let you off at the muellecito (the small public pier). It's across the street from the Supermercado Pearson and next to Hotel Golfito.
If you end up in Golfito with no boat to take, it's not impossible to take some buses that will eventually get you to Zancudo. You'll want to take the 10:00 am or 3 pm bus to Pavones (ask more than one person to find out the current schedule - you'll get different answers from everyone) but get off early in Comte where later in the day (3:30 pm?) a bus will come by on it's way from Ciudad Neily going to Zancudo. Or if you're feeling particularly daring you can try to hitchhike form Comte. Zancudo - A Challenge Getting There and Away. There's information on Zancudo and Paso Canoas and photos on some of the different stops.