WP Business Directory Manager Plugin Admin Listings?

You can test by the admin login name:

$current_user = wp_get_current_user();
$my_user = $current_user->user_login;
if (strpos($my_user,'admin') !== false) { // test for the admin username

if ( !$data->listing_id && ( !$listing_cost || current_user_can( 'administrator' ) ) ) {
    wp_update_post( array( 'ID' => $listing_id, 'post_status' => 'publish' ) ); //update post to publish
        }       
}else{
   if ( !$data->listing_id && ( !$listing_cost || current_user_can( 'administrator' ) ) ) {
    wp_update_post( array( 'ID' => $listing_id, 'post_status' => wpbdp_get_option( 'new-post-status' ) ) ); //let the post in "pendin" position
}
}

Hope this would workout for you.