Goto the URL opera://about and take note of the "profile" path.
Turn off the bookmarks bar and close Opera.
In the profile folder, open the "Preferences" file with JSONedit.
In JSONedit under root/bookmarks_bar, there should be a boolean named "show_on_all_tabs" and it should be set to "false".
Is that value there for you and is it set to false? If it's still set to "true", Opera is indeed not saving your setting.
While Opera is still closed, set it to false and save your changes.
Does Opera work fine then? If not, close Opera and delete the "show_on_all_tabs" object and save your changes. Then try again.
Anyone here use Bitdefender and or Sandboxie? Those are known to interfere with Opera.
Even if you consider this a workaround, going through these tests might help find what the issue is so Opera can fix it.
(Note that the bookmarks bar is supposed to come back on now when you add a bookmark to it. So, if you're just doing that, then that's expected. If you shut it off (whether there are bookmarks on it or not) and it just appears when you start Opera without doing anything, then that's definitely something messed up.)