At first Bilbil protested that he did not want to be restored to his natural shape, saying that he had been forever disgraced in the eyes of his people and of the entire world by being obliged to exist as a scrawny, scraggly goat.

But Glinda pointed out that any person who incurred the enmity of a wicked magician was liable to suffer a similar fate, and assured him that his misfortune would make him better beloved by his subjects when he returned to them freed from his dire enchantment.
Bilbil was finally convinced of the truth of this assertion and agreed to submit to the experiments of Glinda and the Wizard, who knew they had a hard task before them and were not at all sure they could succeed.

We know that Glinda is the most complete mistress of magic who has ever existed, and she was wise enough to guess that the clever but evil magician who had enchanted Prince Bobo had used a spell that would puzzle any ordinary wizard or sorcerer to break; therefore she had given the matter much shrewd thought and hoped she had conceived a plan that would succeed.

But because she was not positive of success she would have no one present at the incantation except her assistant, the Wizard of Oz.
First she transformed Bilbil the goat into a lamb, and this was done quite easily.

Next she transformed the lamb into an ostrich, giving it two legs and feet instead of four.