I've got a Vendor Bill that's related to a Purchase Order. How can I remove the relationship/unlink so the two transactions are no longer related?

if you created the bill from the Purchase order i dont think you can. I would void the bill and create a stand-alone bill if you want them to not be linked together.

Change the vendor in either record then save it. That should remove the link. Then, go back to that record and change it back to the original vendor. But why do you need to unlink them though? But the PO will be considered not yet billed.