Looking for advice on how to market to hospitals.

I run a pretty small operation that provides a very specific service in healthcare. I have no experience marketing to large organizations like hospitals and I feel like I’m hitting a brick wall trying to get in contact with people. I wanted to stop by and leave a card or information with the supply chain manager but this is strictly prohibited in most of their policies.

What are the best ways to get a response from supply chain managers? I understand that hospitals are bombarded with vendors on a daily basis, how do I stand out?