I'm trying to Google a regional airline, but don't seem to be having much luck.
I'm not sure if my last comment posted because it made me register. Oh well.
My brother has traveled extensively in Panama and says you can take a bus from San José to Panama City. I think they run about 35-50. It's about 10 hours and sort of vomit inducing if you are sensitive to that stuff, which I am. That's consistent with what I hear from other travelers. Otherwise, you could look for flights (100-200) on Taca, Copa, or Avianca. about 10 years ago
I did this trip bus bus about 18 months ago and it was very straight forward by road. Book your bus in San Jose, make sure you don't get robbed while waiting for the bus to depart and then sit back and relax on the overnight journey which is in no way vomit inducing. At the border there are people to help you out with your visa and you just give them a buck or two as they really are helpful. Make sure you have a warm jacket or sleeping bag with you on the bus as it gets really cold with the aircon. Luggage gets searched at the border!!! about 10 years ago