A bundle is technically a new product, therefore the process to create a bundle starts with creating new product or a product page with new SKU. The product representation is locked once the SKU is created and when it's connected to some page in the content (i.e. it's not a standalone product, an SKU).
In your scenario, it appears you just need to create that new bundle product and add the products you want to bundle together during setup of this new product, including special price setup.
If you want to list the individual products of the bundle in checkout (cart content listing), you would probably need to create custom transformation function that would loop through the products of the bundle, as this is not available by default.
If you need further advice with this, feel free to ask!