The translucent menu bar is not the only controversial user interface choice in Big Sur. The greatly increased spacing between menu bar items (the icons on the right of the menu bar) also puts space in the menu bar at a premium. You may well not want to give over that precious space to Boring Old Menu Bar.

It is possible to reclaim that space by getting Boring Old Menu Bar to hide its icon.. but of course that also makes its interface inaccessible.

The solution I have found is that you can hide the Boring Old Menu Bar icon by:

right clicking the Boring Old Menu Bar icon in the menu bar
and selecting Hide Menu Bar Item in the menu

The menu bar will disappear immediately and it will only re-appear for 10 seconds every time the application is relaunched.

Now how do I get the icon back?

Now that you got rid of the icon, how do you get it back if you need to make a change in the UI?

Well you need to quit and relaunch Boring Old Menu Bar, but as a dock-less application, it does not show up in the Force Quit dialog, so you’ll have to quit it from the Activity Monitor:

in the Finder navigate into the Utilities sub-folder on your Applications folder
launch Activity Monitor
select Boring Old Menu Bar in the list
then select Quit in the View menu

Then you can relaunch Boring Old Menu Bar:

find Boring Old Menu Bar in your Applications folder and double-click it

You now have 10 seconds before the icon is automatically hidden again, to disable the hiding:

right-click the Boring Old Menu Bar icon and select Hide Menu Bar Item

When you’ve finished you can re-hide the icon in the same manner.

How to hide the menu bar item

Now how do I get the icon back?