My apologies for the late reply. Unfortunately you won't be able to link Work Orders to Vendor Bills since Vendor bills do not sync to QBO. This is why the Bill screen is hidden on a new Method for QBO account and also why you can't find the BillLineItem table in the tables list.
Can you tell me why you will be invoicing your Vendors? What you are looking to do can be achieved with Customers and invoices. Could you create Customer records for the Vendors you'll be invoicing?