I found that volunteering at a teaching hospital is the way to find a doctor you can shadow who may just wind up being your mentor: as a an example I give you my experience:
I volunteered at a major teaching hospital and after working as an ambasador for a couple of months I asked if they could transfer me to a specific dept, which they did. While working their I made it a point to go out of my way to learn everything I could, like by sneaking in to the back of grand rounds and taking notes. One day a doctor walked up to me after rounds and, with an expressionless face, said "My name is Dr. X, One of my residents left, would you like to shadow me?" He was obviously a man of few words but his presence alone was powerful and intimidating. I immediately said yes. Only later did I find out he was the hospital's chief in his practice area and one of the world leaders in his field. I shadowed and volunteered with him for almost a year, including working on his clinical research, until his resident load got too heavy and he told me he could no longer keep me on. When I asked him for a letter of recommendation this year, he called me into his office and let me listen as he dictated it to his secretary; it was the best rec I could have hoped for. Just as I was sending out my completed secondaries, his research was published and got top billing in NEJM, other journals, and on the front page of the health sections of several major newspapers. I can't say for sure, but I think his rec may be a big reason why I have some interviews already.
Anyway, my point is that doctors at teaching hospitals are their to teach. If you show them you truly are committed to learing than they will be committed to you. I hope this helps.