Is "Ptak lata" unacceptable? "leci" implies that it is flying somewhere right? Could you use "lata" to mean that it's just flying around?
You're right, "lata" can be used if it is flying around without a clear destination. That was an oversight on our part, now fixed.
A bird flies - Ptak lata
Mogłoby również być "ptak frunie lub fruwa".