Index: bp-core/bp-core-admin.php
===================================================================
--- bp-core/bp-core-admin.php	(revision 8136)
+++ bp-core/bp-core-admin.php	(working copy)
@@ -399,6 +399,9 @@
 	 * @param WP_Admin_Bar $wp_admin_bar As passed to 'admin_bar_menu'.
 	 */
 	public function admin_bar_about_link( $wp_admin_bar ) {
+		if ( bp_core_do_network_admin() && ! is_network_admin() )
+			return false;
+		
 		if ( is_user_logged_in() ) {
 			$wp_admin_bar->add_menu( array(
 				'parent' => 'wp-logo',