The Moon-Spinners by Mary Stewart

While on a walking holiday through the beautiful, deserted hills of Crete, Nicola Ferris stumbles across a critically injured Englishman, guarded by a fierce Greek. Nicola cannot abandon them and so sets off on a perilous search for their lost companion - all the while being pursued by someone who wants to make sure none of them leave the island . . .

When the big white bird flew suddenly up among the glossy leaves and the lemon flowers, and wheeled into the mountain, I followed it.