Just checked: in Windows 8.1 (and therefore, all versions of Windows 10), the "Don't search the web or display web results in Search" Group Policy works fine in Pro/Enterprise/Education/Business. The "Disable Microsoft Consumer Experiences" one only works in Enterprise/Education, however.

If you are on Home, and don't have gpedit.msc, make a new DWORD in "Computer\HKEY_CURRENT_USER\SOFTWARE\Policies\Microsoft\Windows\Explorer", call it "DisableSearchBoxSuggestions", and set it to 1. Upon reboot Bing will no longer appear in your start menu.