When registering taxonomies for your custom attributes, WooCommerce calls the following hook:

$show_in_nav_menus = apply_filters('woocommerce_attribute_show_in_nav_menus', false, $name);

So, for example, if your attribute slug was ‘size’ you would do the following to register it for menus:

add_filter('woocommerce_attribute_show_in_nav_menus', 'wc_reg_for_menus', 1, 2);

function wc_reg_for_menus( $register, $name = '' ) {
     if ( $name == 'pa_size' ) $register = true;
     return $register;
}