Networking without feeling pushy after 13 years as a bank teller

I want to talk to people in a new field but I hate cold messages. I worry about bothering people. How do you phrase the request?

Follow up with a thank-you and a short update. One of my chats led to a referral a month later.

I wrote three short lines: who I am, why them and a small ask for fifteen minutes. About one in four said yes.