Instagram DM rules, explained

When someone comments, an app can send them one private reply to that comment. It must be sent within 7 days of the comment. After that, the API rejects it.

When a person sends you a message, taps a button or replies to your story, you can message them for the next 24 hours. Each new message from them restarts the window. Outside the window, automated messages are not allowed.

• Messaging people who never interacted with you.
• Bulk DMs to your follower list.
• Logging in with your password to automate the app.

Ask for an interaction first (a comment, a story reply or a tap), deliver value in the first message, and use the 24-hour window for one helpful follow-up rather than many.