It is always nice to have a relationship beforehand with the physician of choice; however, some of us don't have that luxury.
What I did was apply for an internship at a local hospital allowing 120 hours over a three week period. After shadowing many doctors (and building relationships) I was able to have options in the future.
I now shadow one of the doctors regularly, and it was just by dumb luck we were paired. (I'm also shadowing a distant cousin who happens to be a D.O.)
What I'd suggest is going to a hospital's shadowing/education coordinator and ask for some experience with a few different doctors. Then you can slowly build relationships. If that's not available at a hospital around you, then keep calling! Persistence pays off. Doctors are generally understanding of students' want to shadow.