I’ve managed to answer my own question. It’s necessary to add define(‘BP_USE_WP_ADMIN_BAR’, true); to wp-config.php.
I heard we were ‘phasing in’ the wp-admin bar but to be honest I didn’t understand why it wasn’t just standard from the get-go.
Is there anything I need to watch out for, or is this because the admin bar in WP3.3 will behave slightly differently and you’re adding a patch before including this new admin bar as the default?