Previously, bountied questions were available from any question page (including the home page) via the clearly labeled "featured" tab.
I think I actually discovered bounties originally because I was curious what was a "Featured" question was.
With the new navigation, I feel bountied questions have a lot less visibility. They are only indicated by the little blue square in the navigation bar (which I think looks like some kind of admin tool), or by going to the "needs answer" tab and changing the "Show" dropdown.
Simply going back to a "featured" tab is off the table for now (which is why I am declining the solution you propose) :-)
So this question is to try to get ideas about what else we could do to improve the visibility of bountied questions in the new navigation system.