Well let me speculate from a different point of view. The point of view of Gaius van Baelsar.

As he slowly approaches the battlefield on the airship called "Xanthopan" , Gauis receives a report that Bahamut has indeed appeared.

Everything is going according to my plan thinks Gaius and orders his airship crew to prepare the laser cannon thingy (the one from the r46 mission) and the... new magitek contraption.

After the devastating rampage across Eorzea and almost being imprisoned again, Bahamut furiously starts to charge up a Megaflare oblivious to the Garlean airship approaching him.

But before Bahamut manages to finish charging up the megaflare he gets interrupted by a laser cannon bolt fired of Gaius's airship which creates a huge flash (or explosion).

Bahamut is stunned for a few seconds by the blinding white light, but before the elder primal can get his act togheter he finds himself unable to move and finally realizes there is a airship close by with a person on deck who vaguely resembles bahamut's puppet Nael van Darnus. In his hand a mysterious magitek contraption...

A second later bahamut finds himself trapped in a mysterious inescapable place which will later be known as The labyrinth of Bahamut.

As the sun begins to rise the Xantophan sets off to an unknown destination without any care for who is still left behind on the battlefield below.

Gaius while staring off in the distance mumbles to himself: ... time for the experiments to begin...


PS. Xantophan is not the real name of the airship. You can look up on the wiki what Agrius and Xantophan means.
PPS. magitek contraption? spinned it off the experiments the garleans where conducting in The Aurum Vale, Dzemael Darkhold and Toto-Rak.
PPPS. Gaius's experiments? i was thinking of the artwork released a while ago with a creature that had Gaius's upper body and head.
PPPPS. english is my third language, i tried to word it all as best i could! :P