I’m not quite sure about this, but I think this behavior could be caused because of another toolbar. Do you have another toolbar, besides the default Bookmarks Toolbar, installed? If you have other toolbars, try disabling them, and restart CometBird. Now, try it.
If that doesn’t work, close all CometBird windows, hold down the Windows key in your keyboard and press the R key. A small window should appear. Type cometbird -safe-mode and hit the Enter key (this is: cometbird[space][dash]safe[dash]mode). You’ll see the CometBird Safe Mode window:
Check the Reset toolbars and controls box and click on the Make Changes and Restart button. Note that by doing this, all your toolbars customization will be lost and the toolbar’s default configuration will be set instead.
Anyway, I encourage you to provide us with more information about your trouble: when it started to happen, if you installed lately add-ons (what add-ons?), or if you have modified something at the about:config menu, etcetera.