The bookmarks dropdown menu button only appears while you are using the orange Firefox button in place of the classic menu bar.

Normally, it inhabits the far right of the Bookmarks Toolbar. You can drag it to the far left of the Navigation Toolbar (before the Back button). I just tested that and had no problems. However, that is an alternate location: as long as you display the Bookmarks Toolbar, it will appear on that bar.

(The above is based on experimentation, I don't know all the official details.)

(I wouldn't rule out the possibility that someone knows a hack to move the button, so stay tuned for further comments!)

Edited below

What you suggests works for me too but I would like the bookmarks drop down displayed to the left of the back button and the bookmarks toolbar under the navigation tab. For whatever reason, the bookmarks dropdown drags itself to the right most when the bookmarks toolbar is also enabled. See attached screenshots: 1 is what I want but 2 is what I get.

Thanks for replying!

If you want the bookmarks menu button to appear when the Bookmarks Toolbar is visible then you need to place that BMB button with the drop marker on the Bookmarks Toolbar to the left of the "Bookmarks Toolbar Items" item.

I have been reading through the forums and found through another posting that what I want is not possible through Firefox options. I used this add on and it does just what I want it to do! https://addons.mozilla.org/en-US/firefox/addon/bookmarks-menu/