Problem with open_basedir restriction in effect
Another potential cause is that Civi's WordPress.php file is incorrectly guessing the path to your WP install. You can force the path in your civicrm.settings.php file, like so:

define('CIVICRM_CMSDIR','/home/bmeeco/public_html/wordpress');

Edit: I think you've actually found a bug (CRM-14987). The way it guesses the WP path can cause warnings (it's almost guaranteed to if you are on cheap shared hosting). My solution will get you by, however.