I just started my shadowing today and I got it by randomly emailing different physicians. I went to my local hospitals website and looked through the different specialties that I was interested in and gathered 12 email addresses. I emailed the doctors telling them who I was and I was interested in shadowing them but understood as physicians that they were busy and understood if it was not possible. Out of the 12 emails I sent I got 5 responsed; 1 doctor said he wish he could but was unable to because of a new position he took up. 4 other doctors were happy to have me shadow. 2 Pediatricians, 1 Orthopedic Surgeon, and 1 being the Chief of Cardiology.
Don't be afraid about blindly emailing them, as long as you are sincere with your email it should not be a problem at all in any way. I shadowed a pediatrician today who taught me a lot, she was very nice, sincere, and helpful; explaining about the cases and patients. If you have any questions, feel free to PM me.