Sorry if my question is stupid, is there a way to add a custom button through a UserEvent Script to a saved search? We want to enable the user to make an action "Create a Bill" based on the content of the search.

No. You can either create a suitelet that displays the search and button, or a link on every result row of the saved search

God, I didn't think about that. So the suitelet doesn't have to build up the search right, we could use the one we already built using the front-end.

Yup you can load an existing saved search

Got it, thanks very much 😘