Bahamut, like every other Final Fantasy XIII eidolon, transforms in gestalt mode. A plain old dragon seems appropriate. Mecha Bahamut would be an OK too. If Mecha Godzilla exists why not Mecha Bahamut?
That’s probably too logical.
So, when Bahamut switches gears into driving mode it turns into a flying dragon (that looks more like a flying beetle to me) that Yun Fang can ride.