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We can enter the bill date and the bill payment date by recording a bill and a payment transaction since they both have a date field. Let me guide you through creating these transactions in QuickBooks.
Create a bill:
Click on +New and choose Bill.
From the Supplier ▼ dropdown, select a supplier.
From the Terms ▼ dropdown, select the bill's terms.
Enter the Bill date, Due date, and Bill no. as they're recorded on the bill.
Enter the category details or the item details.
When you're done, select Save.
Pay the bill:
From the bill transaction page, click on Make payment.
In the Bank/Credit account field, choose the account where the money is taken from.
Enter the Payment date.
Enter the amount in the Amount field.
Click Save and close.
If you would like to see more references about handling bills, please refer to these articles: