Open up the Bookmarks sidebar (keyboard shortcut Command+B), you can then select the separators by clicking on them, and then press the Delete key.

I tried but did not delete them. I also tried clicking on the separator and right-clicked then chose delete, which did not help, either. Appreciate any help.

Open the Bookmarks Manager and select the Bookmarks Toolbar folder in the left pane.
Then you can easily remove separators on that toolbar in the right pane.

• https://support.mozilla.com/kb/how-do-i-use-bookmarks

Just Press "Ctrl + B". You'll see Bookmarks menu on Left side of screen. Here you go. Remove all unwanted separators you wish to remove by selecting and deleting them.

I am still running XP, and here's how I get rid of extra separators :

Open the "Bookmarks" tab in the upper toolbar like you normally would. Click "Show all Bookmarks"- this opens a frame called "Library". You will see two places named "Bookmarks Menu". Open either one of them and you will see a version of your bookmarks list. Scroll down and right-click the separators you want to delete.

Gosh, there's the option to delete them !  Go ahead and do it.

Why you can't just delete them in this very same manner from the list that you normally use is a mystery to me, but for some reason you can't.