Right-click file in MusicBee, choose Edit, hit "Rename" at top of edit window, change name as desired in File Organiser window.
If for some reason you still prefer to edit/rename the file in Mp3tag, add that application to your Preferences/Tools/External Applications list, and it will show up in right click/Send To/External Tools--or, create a shortcut to same for faster access. Note that if you don't rename/edit using MusicBee itself, you'll need to rescan for the Library to pick up the changes. That will be done automatically or at MB startup (depending on how the option is set) if the file is in a monitored folder (Prefs/Library/monitored folders).