One of the basic reasons that I came to Bocas del Toro and made the decision to begin development is the proximity to the US.  There are short,  cheap flights from many major cities throughout the US and Canada, as well as Europe.  I just took a direct flight from San Jose, Costa Rica to Madrid late last year.  Check for flights into either San Jose, Costa Rica or Panama City; Panama City is easier, but there is sometimes a significant price difference.

The local airport has expanded to receive direct international flights sometime in the future.  Copa Airlines is talking about this and the plan is to get direct flights to Bocas from Miami, New York, Los Angeles and wherever the hell else will send a flight to a cow pasture.

From Costa Rica:

From Costa Rica you can fly http://natureair.com/ direct to Bocas, but will almost definitely have to spend the night in the shit-hole known as San Jose on both ends of your trip.

There are buses every couple of hours from the Caribenos bus terminal to the border, about 6 hours.  And there is one Bocatorenos bus everyday at 9am from the “anitgua Copa”/Bocatorenos bus stop that makes it into Panama.  In both cases you will get a 30 minute taxi to Almirante once the bus eventually stops and catch a boat taxi from there to Bocas, those are running constantly.

From Panama City:

From Panama City the bus ride is a horrible 11 hours, but can be done overnight from the Albrook bus terminal.  The domestic flights are from the Albrook Airport and http://aeroperlas.com/ and http://flyairpanama.com/.