I spent some time trying to figure out why my external page couldn't bootstrap with Drupal, despite me following suggestions from lots of forums. I eventually got it working the following way, figured I'd post the solution here incase anybody else had the same issue. Hopefully someone will find it useful and not lose 4 hours trying to figure it out:

If the other solutions have not worked (including trying to change "chdir") then try this instead:

 define('DRUPAL_ROOT', $_SERVER['DOCUMENT_ROOT']);
      $base_url = 'http://'.$_SERVER['HTTP_HOST'];
      require_once DRUPAL_ROOT . '/includes/bootstrap.inc';
      drupal_bootstrap(DRUPAL_BOOTSTRAP_FULL);
      global $user;