BigBusiness adds fields for 1 line of Ship Method with "shipping_lines/method_title".
Ship Method is not included in Automatic mappings. So, go to Connect toolbar, Woo, select an import, highlight entries on left and right, click Insert and then click Save As.
After saving your mapping, use it in the Woo tool for importing batches or select it for Import Orders in WooCommerce Settings to have it run when using the Auto-Connect.