Wikipedia reports that Griechische und Albanesische Märchen contains a Greek Donkeyskin variant that involves a burrowing bed.
In a Greek variant from Epeirus collected by Austrian consul Johann Georg von Hahn with the title Allerleirauh, a widowed king declares he wants to marry his own daughter, despite her protests. To delay him, the princess asks him to fashion her two dresses of gold and a bed that can furrow through the ground to reach any other place. The king gives her the requested items; she takes the dresses, some ducats for money, jumps on the bed and goes to another city. The city's prince, during a hunt, finds the princess, wrapped in furs, in the forest and takes her in as a goose herder. Some time later, this prince holds a grand ball, and the princess attends it with her dress of gold. She dazzles the prince, but escapes the ball back to her low station, and throws some ducats to delay the prince. He becomes interested in finding her, so he holds two more balls. After the third ball, the princess loses one of her shoes and the prince tries it on every maiden, but cannot find its owner. At last, the princess, still wearing her golden dress underneath the animal furs, goes to bring some water to the prince, and he recognizes her.
I can't read German especially with that typeface, so is such a story located that where Wikipedia says it is, in "pp. 151-154.", or anywhere else in that book? Which I can't figure out with that book being 710 pages long while also being split in two and resetting page count here?
Also, Wikipedia's page on Allerleirauh, a.k.a "All-Kinds-of-Fur / Thousand Furs" makes no mention of the burrowing bed.