I'm lucky because I know docs from my ballroom dancing class. I'll admit it, yes I take ballroom...but it stictly 'cause the chicks dig it! I swear! lol 🙂 Kidding aside, you'd be surprised what activities doctor's like to get involved in. I've met a couple through this social interaction. This is often a better approach than stalking them around the hospital. Get to know them outside of the hospital. I did and it's been a fabulous experience. If you can, try to become friends with them. Plus, I sent a letter to another doc about shadowing. He was an osteopath just for the record. He called me a week later. He told me that not only would I get to shadow him, but his colleagues...one of which is a thoracic surgeon, who by the way, performed a lung transplant that's only been done 15 times in the world! I was like WOAH!!! 😳 Writing letters and sitting tight is another way. Also, be persistent about it. Let them know your desire and it will take you far.
Good luck