Rae from Shopify here. Thank you for reaching out for more information on applying discount codes to specific variants in bulk, and welcome to the Shopify Community!
While there are several other apps that can be used to create discount codes for specific variants, I recommend reaching out to the app developer from the bulk discount app that you're currently using to find out if this feature happens to already exist within their app. In some cases, features may be difficult to find at first glance, so if this feature exists, the developer can certainly help you find it. To contact the developer about this, just follow these steps.
If the app you're using now doesn't allow discount codes to be assigned to specific variants in bulk, then I suggest looking into another app that can be used for this instead. Excelify is a great option that outlines specifically how to create discount codes through their app for certain variants here. Another app that offers this functionality is Bulk Discount and Sales Manager.
Please keep in mind that these are third party apps that are supported by external developers. So with that being said, if you have any questions about setting up variant discounts through these apps, or about the billing associated with using these apps, make sure to reach out to the app developers about this directly so that they can help out further. These individuals created and developed these apps, so they're the best people to speak with about any support-related questions you may have.
This information should get you on the right track, but if you have any other questions or concerns, please let me know and I'll happily assist further!