If possible please share your store URL and where I can add product to the cart with bundle product so I can check with that.
There might be a chance that if you used the bundle app which is generate a draft order then it is chance that the discount code box is not display on checkout.
@socialmealprep , do you mind elaborating on your question? Is the reason you want to be able to enter a second code is so the discounts can somehow “combine” and give a bigger discount to the customer?
From what you’re describing, it sounds like you’re looking to stack discounts, where a discount code can be applied on top of a bundle that already has a discount.
You can check out ADU: Automatic Discounts for this. It lets you enable multiple discounts to be stacked, so your customers can use the discount code even after a product has already been discounted. This should give you the flexibility you’re looking for.