To create a new directory, right click on the desired parent directory in the directory list of the file browser in the side panel and select New Directory. You may also right click on any file in the files part of the file browser.
Then enter the desired name in the Directory name dialog. Bluefish will create the named directory with the default permissions under the currently selected directory.
Note that you cannot delete directories within Bluefish, but you can refresh the view with the Refresh contextual menu item of the directory part of the file browser if you delete them externally. This is especially useful when you add files and directories or delete files.
If you right click a directory in the file browser within the side panel, you can make this directory the base directory for the file browser using the Set as basedir option. Then you can access it directly from the pop up menu in the upper part of the file browser.
By default the file browser follows the document focus. If you change to a different document, the file browser will show the contents of the directory where this document is located. This behaviour can be changed by unchecking Follow focus on the bottom of the file browser.