In 1709 and earlier, you can set the group policy “Allow Cortana” to disabled to disable Cortana and completely eliminate any Bing search results and suggestions when using Windows Search.
In 1803 Pro, this policy no longer has the effect of disabling web searches and suggestions. Enabling the additional policies “Do not allow web search” and “Don’t search the web or display web results in Search” has no effect on this either.
There is seemingly no official way to prevent web searches and suggestions from appearing in Pro. This has been the case in Home for the last few releases. Education and Enterprise are unaffected and can still make use of these policies.
Results previously: https://i.imgur.com/2HhhtwM.png
Results in SCU/1803: https://i.imgur.com/zS2Pqlx.png