When you configure a bundle product using "Package files from other products/affect their inventory", that doesn't actually add the other selected products to the buyer's cart; it just creates a single product that the buyer can add to their cart, which after checkout would issue multiple download links for files you'd already uploaded for other products.
If you're seeing multiple items in your shopping cart, that's because you'd previously posed as a buyer adding those items to your cart, so if you didn't remove them, they'd still be in your cart. Other buyers coming to your site would start with their own, empty cart. We remember each buyer's cart contents for up to 24 hours after their last cart view (or up until they complete checkout), so they can come back to their cart up to a day after shopping on your site and complete their purchase without having to start all over again.
You may be interested in this help page explaining how the behavior of online shopping carts are designed to mimic a real-world shopping cart in a physical store: