To save the doc in google drive, click on 'Document'->'Save As'->'Save' beneath Google Drive. This article explains it in detail, http://mindmapmaker.org/using-google-drive-with-mindmaps.html
Check for one thing, after saving to google drive, it shows 'Saving to Google Drive...' at the top-left part of windows. After the document is fully saved, it again shows, 'Saving to Google Drive...100%'. After this new notification only the document is saved in google drive. If it is not coming up means, the file is not getting saved in google drive for some reason. If this is the case, please try another browser like firefox or IE.
'Share via Drive' only functions if you have saved the current map in google drive.
Let me know if it works now.