Upgraded Drupal 7.37 to 7.38 using Drush and its not working. update needs a higher bootstrap level to run - Error
Make sure your Drush commands are issued from the appropriate subdirectory of your website (change to the directory where your Drupal site is installed and try again).

So try navigating to the sites/default folder (assuming this is NOT a multi-site, is it?), and then retry your Drush comand ... Seems that is what is causing your problem ...

If that doesn't help, it could well be an issue with the version of Drush that you are using. Would it be an option to downgrade to a lower version of Drush? FYI: Drush 6.x does support D7 also ...