You can configure your email sending with a reply-to email (example customers@mydomain.com) and not have auto replies or bounces go to that reply-to address.

The auto replies will go to the envelope sender email. I prefer to set that to something like email@mydomain.com rather than noreply@mydomain.com because noreply just looks so unfriendly.

Replies from real people will go to the reply-to email (customers@mydomain.com) and bounces/auto-replies will go to the sender address (email@mydomain.com). You can then write a script that automatically clears the auto-replies and handles the bounces from the email@mydomain.com inbox.

This will allow you to still handle real customer inquiries that come into the reply-to email without being bombarded with bounces and auto-replies.