Installed Bluez theme as a sub-theme but can't change Appearance Settings
In one of your comments you wrote you created your my_bluez folder within the "sites/all/templates folder".

If that's really the name of the folder where you created the my_bluez subfolder (i.e. that it is not a typo in your comment here), then I wonder what result you would get if you would rename that folder to "sites/all/themes". Because that would make it comply with the Community documentation about Installing themes (bullet 3 in that list there). It would make it even  harder to realize for Drupal that my_bluez theme is actually like a clone of the Bluez theme, no?. Just to be sure, after renaming that foled I'd then also clear the Drupal cache.

If that still doesn't work, then I wond if it could be related to some (missing) file permissions of that newly created folder.

Does this help somehow?

PS: Creating a "clone" seems to me like a better term of what you're trying to achieve. Creating a sub-theme is really something related to base themes in Drupal-eze.