Is it possible to predict where and when Beedle's airship shop will show up? If so, where and when will he appear?
His shop moves in a clockwise motion around Skyloft's Bazaar during the day. It resets to its starting position over the Plaza near the Tower of Light whenever you enter Skyloft.
At night, his shop doesn't appear in Skyloft at all... instead, it's docked at Beedle's Island, in the upper-right corner of the sky map.
You can check your map to see where it's currently at in Skyloft; it shows up as an icon of Beedle's face.
Beedle make an orbit of the bazaar on Skyloft Island starting very early in the game (you more or less need an item from Faeron Woods to ring the bell to get into the shop). Like all shopkeepers and minigames, his face will show up on the map telling you where he is.
At night he is on his island (Beedle's Island) in the northwest corner. If you go to sleep on the bed in his shop and get up at night, you will wake on his island. You need to do this to get one of the Goddess Chests on the island.