Will the discount be applied twice if the bundle is added twice?

No, if the same discounted bundle is added to the cart twice, only one Frequently Bought Together discount will be applied to one of the bundles.

However, there is a case where this doesn't hold true, as explained in the related article.

Let's look a few examples.

Non-combinable discount

If a Frequently Bought Together discount is set as non-combinable on the preferences pages, when the same discounted bundle is added to the cart twice, a discount will only be applied to one of the bundles.

For example, in the following checkout image, where a 10% discount has been configured, you can see a $100 bundle added three times and how the discount ($10) is applied to just one of the bundles.

Here is another example where the "Cheapest item for free" discount has been configured and a bundle has been added three times. You can see how just one of the cheapest products is free:

Combinable discount

If a Frequently Bought Together discount is set as combinable on the preferences pages, if the same discounted bundle is added to the cart twice, a discount will only be applied to one of the bundles. As explained at https://help.shopify.com/en/manual/discounts/discount-combinations#examples. However, there is an exception to this due to a known Shopify limitation: if we add the same "Cheapest item for free" discounted bundle twice, the discount will also be applied twice.