If you want your printed checks to show the vendor bill number for which you are making a payment, you can add the Bill Number manually to the Memo field in the check. To do so, open the check details from the Bill Payments or Checks screen and then add the memo. The memo shows up when printing the check.
Another option is to use the Check Style Voucher Details when printing the check. This style includes the Bill Number on the printed checks. Check CORE Help Center for details.