You can change your payment method — as long as your buyback order hasn't been marked as “Processed”. You can do this directly in your account through a simple self-service process. PayPal payments are processed almost instantaneously to the linked email account once reissued. The payout methods available for buybacks are PayPal and Mailed Check, so you will need to select one of these options during the update process.
Prior To Order Placement:
You can change your payment method for each buyback order you place during the checkout procedure. The available payment methods during checkout include PayPal and Mailed Check.

After The Order Placement:
Log in to your BooksRun account.
Go to the “Buyback” section.

Select the buyback you want to update.
Check the order status under the “Order Summary” tab.
If the status is not “Pending payment” or “Paid”, continue.

Find the “How we pay you” section.
Click the “Edit” button next to the payment method.
Choose your preferred option:
Check
PayPal (enter your preferred PayPal email)
Click “Save” to confirm the update.

If your order is already "Pending payment" or "Paid", the payment method can no longer be changed. For international sellers, please note that the only available payout method is PayPal; mailed checks are not an option.
If your payment method is a mailed check, please note that checks are issued within approximately four business days after the order is processed. Additionally, you will receive a confirmation email once the check has been sent.
Related Questions:
How to switch my payment to PayPal (check)? ; How can I get paid for my buyback order? ; When will I get paid for my buyback order?