Title of this book with dragon and girl?

I was at hastings the other day and wanting to waste time I grabbed a book. The book began with a girl in a different world i think but very similar to earth, she wanted to adventure to the border where the dragons were. Upon making it there she climbs the cliff only to fall into a river and get rescued by a dragon, when she wakes up she thinks the dragon is going to eat her but instead it talks to her and thats about as far as i got. Anyone know the title to this book? I would like to read it but can't find it. Help appreciated