By default, Bundler uses Shopify Draft Orders to apply bundle discounts. One of the limitations in Shopify is that you can't send abandoned checkout emails for Draft Orders.
To bypass this issue, you can turn on the feature to apply the bundle discounts with discount codes (not with draft orders) in your shop. This can be turned on in Bundler -> Settings -> Discount modes.
This will allow you to send abandoned checkout emails to your customers.