When is it appropriate to run a drupal_bootstrap?
In order to bootstrap Drupal from another PHP script, you can use below code:

 define('DRUPAL_ROOT', '/path/to/drupal');
  require_once DRUPAL_ROOT . '/includes/bootstrap.inc';
  drupal_bootstrap(DRUPAL_BOOTSTRAP_FULL);


When ever you would like to call Drupal Functions or features outside of Drupal root you can use above code..