Hey Jonathan,
We actually understood what you want and how the apple menu bars because we have re created that menu in our local testing servers. I think that you though that apple menu only has one menu but it is not. As matter of fact, @christian’s suggestion is exactly what is happening in apple menu. In the homepage, there is one menu exclusively for the homepage.
And when you click on the links above, you will be redirected to the next page with a different set of menus:
What you have seen in the apple menu is actual different set of menus for each pages. You just do not noticed that you are actually going to the next page because the page loading is pretty fast.
As @Christian suggested that you will create two sets of custom headers. The first header with your bar 1 will be used for the homepage. The second custom header which is more likely duplicated from the first header will be assign to several other page and also edit this header for you to add the second bar. This is how apple menus works.
_So when you click on a link in 'Bar 1', 'Bar 2' appears with the sub menu and so on._
What you wanted may not be possible as of this moment. It might need custom JS/CSS which is already a custom development and way beyond the scope of our support.
Hope this explains it all.