This is a faked up story: Some years after Bilbo's journey with the dwarfs Fili and Kili came to visit him. They took a Took, Polo and Mary with them. While Mary was cooking, the "boy" plays hide and seek.
The hiding place from the Took were the mushroom and realy simple indeed...
So he lay down and sterrte in the sky.
The dwarves were not hidden so well, but for their art typically in the rocks
Polo found the dwarfs and Mary almost finished with cooking
Marry asked loud: "How do you like the ostrich fried egg, Bilbo?" "Sunny side up!" he replied. Polo know now where he was, do you know it too? (Bilbo is not using the ring :-)