Resolved ... Windows 10 Build 10586.36
firefox 43.04 chrome 47.0.2526.106



Determined to find out how Bing was being restored in firefox,
I used sysinternals "procmon" to trace firefox...

If you're interested in saving screen real estate, and extra toolbar line doesn't do that.

I drag the search bar to the toolbar menu at the top, to the right of "Help".

And ... I still cannot...