In the Hero’s Journey, the hero is an ordinary person who embarks on a journey of self-discovery to become a hero. In The Hobbit, Bilbo is a happy-go-lucky and somewhat hapless Hobbit who ends up going on an adventure because his friend Gandalf the wizard needs a burglar.
The hero’s journey always begins with a call to adventure. The hero can either reject or accept the call. More often than not, the hero (who is not a hero yet) rejects the call. Bilbo rejects Gandalf’s request, and Gandalf leaves a note on Biblo’s door for the dwarves. Bilbo is much more interested in eating and drinking than in adventures, but Gandalf does not allow him to reject the call to adventure.
Gandalf is Biblo’s mentor for several reasons. First of all, he is the one that presents the call to adventure to Bilbo and does not allow him to reject it. He also starts Bilbo on his journey, and throughout the journey he provides him assistance. In order for the hero to grow he needs to separated from, and then reunited with, his mentor. Gandalf leaves Bilbo but does return later.