Those are published data sources. Whether or not Bridge is used to refresh the data is irrelevant to that screen.
If you don't want a data source to appear on that pane, delete the data source from Online.
If you want to keep the data source but prevent users from seeing it on that screen, I do not know of a way to do that.
How do I delete the data source?
I think you have to delete that datasource from tableau online
Are you an Online admin?