Eire (The Rider Chronicles Book 1)

Eire is the last gryphon of his world, and has spent hundreds of years in ours, waiting from inside the shell of his egg. He's been waiting centuries for the right person to become his bondmate and fulfill the prophecy that will return balance to his realm.
Sixteen-year-old Ashling Walsh came upon the “stone” by chance, and fell into a world of magic where Man–once banished for his evil deeds–is prophesized to return to restore the world to the way it once was.
There’s just one problem: the chosen young girl from Dublin only wants to return home, and has no interest in any sacred mental bond. On a journey into this strange new world alongside her childhood friend Casey and an Elf warrior-in training named Bynami, Ashling will find great bonds can be formed even without the help of magic, and others can be severed with the swing of a sword.