Either I am stupid or you're being dishonest. There is no one click way to disable it.
Only on pro versions of windows, with a group policy otherwise a couple of obscure registry keys no regular users know.
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Type something in the Start menu
Top right meatballs menu button
'Search settings'
'Let search apps show results' -> Off (or disable only Bing)
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I don't know about the Home edition.
You can also launch that Settings page by running in powershell:
Start-Process "ms-settings:cortana-windowssearch"