When a customer creates a bundle and proceeds to order it, they should be redirected to your cart page by the app by default - even if the theme is set to use the cart drawer by standard. This is because Bundle Builder was designed to integrate into the theme's Cart Page primarily.
This includes the any type of Mini cart, AJAX Drawer, and pop-up types, so you will need to ensure that this process is completed, before using the Bundles with your desired Cart type. The Cart Page template is standardized across all Shopify themes, so the app's coding can easily and immediately integrate into this as needed.
If the Shopify theme has a cart drawer option, this is a feature of the theme and uses a coding setup specific to the theme in question. Sadly, these cannot be used without a custom integration. If any issues occur with the appearance of the Cart drawer after installing Bundle Builder, please contact your theme developers if further assistance is needed.