Rosemary,
I have a solution for you.
1. re-open your web map and switch to the Map Viewer Classic.
2. check that your bookmarks are still there
3. save your web map
4. now go back to your WAB configuration screen.
5. remove the bookmark widget
6. click save
7. re-add the bookmark widget.
Your bookmarks should appear. You will also be able to add new bookmarks in the app.