Cold messages to people in my field, do they work? - first time posting

I sent 4 messages on a professional network and got two replies. I do not usually post, so bear with me. 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.

Do not apologise for asking. Most people remember someone who helped them.