Can't confirm it exists, but there's talk of a new Airport Bus--an option besides bus and taxi:
"newly launched Airport Bus, where 9.90złtickets can be purchased direct from the driver (euros accepted). Catch it from the bus stop to the right of the terminal building, and find your journey terminating outside the Hevelius Hotel (return journeys back to the airport available). Times as follows:
From the airport 09:50, 10:50, 11:50, 13:10, 14:45, 16:05, 18:25, 19:50
To the airport 09:00, 10:20, 11:20, 12:30, 14:00, 15:20, 16:50, 19:00"
http://www.inyourpocket.com/poland/gdansk/arrival-transport/Arriving-by-plan... -Jodi