I have elaborated on the steps here:
1. With the Select tool active, interactively select the annotation features in the map (alternatively, highlight rows in table)
2. In the Attribute pane, highlight the annotation layer name in the treeview for bulk editing
3. Update the attributes and apply the edit
4. Do not clear the selected annotation features by clicking Clear Selection on the tab or some other way
5. With the Select tool active, update annotation selection by interactively selecting features in the map (or highlight rows in table). This will update the selection list of features in the Attribute pane treeview and will keep the annotation layer name highlighted from step 2 for quick bulk editing.
If you clear the annotation selection, the Attribute pane treeview will default back to highlighting the first feature identifier in the list of selected annotation features.
Hopefully this helps clarify. If not, I will work on a video.