Hello Sara Taylor
There is not another way in the product to link a bill to an to an estimate/invoice without having the full access to be able to convert the estimate to invoice and from estimate to purchase order/bill.
We are not aware of an app which would integrate with QuickBooks that would do that you can look at the apps section just make sure the flag is set to the UK.There may be an app outside of our apps section you could use that other Community users can recommend.
Emma