Hi Markus,
There is not a built-in way to do that, it is not integrated with the Media Library.
What you can do manually is one browser-tab open in the Media Library. On the list view there is an action for each item “Copy URL to clipboard”, which is the URL of the image. You can enter that in the popup for BBcode images.
Alternatively, on the view with a single image, there is the field for “File URL” that you can copy.