Shopify Buy Button is a separate channel, which can't be affected by Bundler. However, we do have a feature on the premium plan, which allows you to show the bundle widget on third party pages (where you also use the Buy Button).
You can read more about this feature and get all the necessary instructions in Bundler app -> Show widgets outside Shopify.
With this feature, you can display the bundle on any third party page. When the customer clicks on the add to cart button in the bundle widget, they will be taken directly to the Shopify Checkout, where they will be able complete the bundle order.
However, you have to know that when the customer clicks on the add to cart button in the bundle widget on a third party page, the bundle products won't get added to the Shopify Buy Button cart, nor will the other cart items be included in the bundle checkout. This is so due to some technical and security limitations, which prevent us from accessing the Shopify Buy Button cart.