Add Notes to Bulk Updates
You can add (and send) automatic replies to all contacts in a bulk update, but you can't add a private note to the bulk-updated-tickets.
But it would be so easy... just un-tick the check box for "send from..."
You can use Scenario automations to add bulk private notes. Here's how :
Now you should have an existing scenario created with the note that you'd like to add. In the screenshot below, notice how the option to add the note as a private one is checked.
You can go ahead and select the scenario that you have now created from the ticket list view page to update the tickets.
Hope this helps.