Hi upsidedownhat, thanks for posting on the Community
When you have a customer who is also a supplier, you can record a contra transaction using a journal entry to offset the bill and invoice.
To create the journal, select + New > Journal entry, enter the date and choose the default Debtors account (or Accounts receivable) on one line (with the customer selected in the Name field) and the Creditors account (or Accounts payable) on the second line (with the supplier selected in the Name field). Enter the amount in each line and save.
You can then link this to the invoice/bill by selecting receive payment/make payment, where the journal will show listed under Credits to apply.