Check for connections being made by SearchUI.exe over HTTPS to Bing servers. A tool like TcpView or Wireshark should do the job.
If you really don't have these being made, please share with us your settings, anything you suspect may have disabled these? I've been unable to find anything and I've applied the tweaks from this article, including the GPO changes:
I can confirm this: it also does not happen on my machine.
However, it does download some app images that are displayed in my start menu for apps that are advertised in a "play and explore" category in the Start menu.
If I select Settings in the search menu it says "Online search isn't supported in your region". I can enable Online Search, but even then I need to explicitly select "Web" as opposed to the default "My Stuff" before it opens a browser and connects to Bing.
This machine including privacy settings was migrated from Windows 8.1. When I installed that I selected custom settings and disabled most of the privacy sensitive settings.
Just FYI, Microsoft has one of the clearer Privacy Statements. It's organized by service and provides an overview and then the option to drill-in. You might get some answers in there:
This is not happening to me either. I have disabled many things in the Settings => Privacy menu, I guess it might be related to Cortana (Settings => Privacy menu => Speech, inking, &typing), but I am not enabling it to find out.
I have the default search settings.