Bahamut is found in the secret deep-sea research facility, which is similar to round island from FF7 in that it is invisible on the radar. It can be found to the far south-west, but can only be entered if you have the Ragnarok. You can come here in Balamb Garden, but you will not be able to enter the facility itself. In order to get Bahamut, you need to reach the glowing blue light in the middle. However, walking whilst the blue light is flashing will automatically engage a random encounter. Once you have reached the light, you will be asked questions. The correct answer will trigger a certain battle each time.
You must answer "It is not our will to fight" for the first, "Never" for the second, but for the third question, there is a third, hidden, response that you must select. If done right, you will now fight Bahamut. Defeat him to unlock him as a GF.