If you are using the Library window (Manage Bookmarks or Command+Shift+O as in Organizer), you should be able to drag and drop. There are some situations where dragging copies instead moving, meaning you have to go back and delete the duplicates. I haven't used it enough to know the specific circumstances.

I think I see what's happening. In MacOS, in most apps a successful drag is usually accompanied by a green plus arrow that you can use as an indicator that a drag-and-drop is going to be possible. But when I do a drag-and-drop for a bookmark from Manage Bookmarks, though it looks like the drop does happen, you don't have that green arrow to indicate that it's possible and is going to happen. Also, that arrow guides you to visually see the destination so it's a little disorienting without it.