Networking without feeling pushy after 5 years as a bank teller

A friend suggested informational chats and I do not know how to ask. I worry about bothering people. Did any turn into leads?

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.