Bulk Discounts Now does not currently support the use of dynamic checkout buttons, including unbranded (Buy it Now button) or branded (Shop Pay, PayPal, Google Pay, etc.).
As a result, discounts will not be applied if the express checkout button is used, as the app relies on the Shopify Draft Order API to provide discounts, and using the express checkout buttons does not create a draft order as needed.
However, discounts will be applied if you use these buttons on the checkout page only.
To avoid issues regarding discounts, it is recommended to hide the express buttons on your product and cart page.