Make the Arduino look like a bluetooth keyboard to enter the data in text.
This may be difficult because most bluetooth modules available for the Arduino don't support the HID profile but only the serial profile. If you take the more expensive modules you may end with a price higher than the Kestrel station.
I'd try to contact the developer of Shooter (seankndy) and ask him what the plugin interface is. I'd bet that this is a much more reliable way to connect to his app.