I've flown to and from Bocas a number of times. As a matter of fact, my wife, two friend and I are going there a week from today.
There's no problem flying Air Panama to Bocas. Since Aeroperlas pulled out of Panama, Air Panama has increased flights to and from Bocas. And, it looks like Copa will also begin flying there from Tocumen.
Aeorperlas was a part of TACA ... one of the worst run airlines in the world. (Check out the forum comments on Trip Advisor.) Panamanian regulations dicated that the two airlines, Aeroperlas and Air Panama, had to charge the same rates for their destinations. Aeroperlas said, "It's not in our business model" and pulled out on February 29. We originally had reservations for this trip on Aeroperlas. Fortunately, I was able to get the charges refunded and get new reservations on Air Panama.
As far as service, there was really very little difference between the two airlines. Their flight schedules were within a couple of minutes of each other for nearly every destination. Their equipment was/is very similar -- turbo props. For delays and cancellations - not much difference there, either. Once in David and once in Bocas, when it looked like my Aeroperlas flight was going to be late, I changed my ticket and got the on-time flight on Air Panama.
You can get much better service out of Albrook (aka Marcos Gelebert) than out of San Jose via Nature Air. Nature Air only flies to Bocas two or three times a week. Nature Air flies a much, much smaller plane. Which means if they're approaching the weight limit, guess what's gong to be left on the tarmac? Your dive bag. Good luck getting it from Costa Rica to Panama. When you get to Bocas, you'll also have to deal with immigration, paying for a tourist card and coming up with the $40 (cash only) exit fee. Fly Air Panama ... take an extra day in and around Panama City and see a little bit more of the country before or after visiting Bocas.
Air Panama's website is in English -- even when purchasing your tickets. (Aeroperlas old site turned to Spanish only during the ticket buying phase.) But, if you're buying tickets more than six weeks out, you'll get a notice that flights aren't available. They doesn't necessarily mean they're booked. It's more likely their system is overloaded. If you continue to have trouble, contact the place where you'll be staying, either in Panama City or in Bocas, and ask them to book your flights for you. Most hotels and B&Bs will do this.
When you get to Bocas, there is one dive operator that stands out over all the others; Bocas Water Sports. Besides being a PADI 5-Star facility, they have the best instructor/DMs of any operator I have dove with anywhere in Panama. Panamanians aren't noted for a high degree of customer service/customer focus. BWS is.
I hope you get a chance to see and dive Bocas. If you like macro, you'll love it.