The Bypass Users feature's functionality is to limit unnecessary users from triggering a dynamic share. This feature is useful especially for Salesforce users that are loading large records via Data Loader and subsequently do not want the records to be dynamically shared.
This feature is located within the Dynamic Share Trigger Builder Properties page. To use the trigger bypass, enter the email of the user you want to exclude in the Bypass Users field. Once the properties page is saved, it will take effect immediately and all Dynamic Shares will be bypasses for the users specified.