First, bear in mind that a "bundle" product (one which uses the "Package files from other products, affect their inventory" setting) is a completely separate, independent product; it does not work like actually ordering each the individual products selected for the bundle. The bundle product can simply issue download links for files already uploaded to other products, or affect the inventory count for other products that use Inventory Control, and that's all that setting does.
Bundle products cannot affect the inventory of other products that use "Variants having individual price/weight/stock/SKU", as there's no way for the bundle product to identify which particular Variant of the component product should have its inventory affected. Bundle products can only affect the inventory count for other products that track a single, general inventory count for the entire product.
Bundle products also cannot use Variants or Variations of their own to determine what other products to affect or how; whatever products you select in the list when you enable "Package files..." will all be affected by purchases of the bundle product.
The typical way of allowing buyers to choose from several existing products for their order would be to paste your Add to Cart buttons for those products into your page. The buyer would click Add to Cart for the items they want, then they would be able to take just those items to checkout together. This is designed to work similarly to a shopping cart in a real-world store: