Disable Cortana Using Group Policy Editor
To disable Cortana in windows 10
- Press Win + R keyboard accelerator to open Run dialog box.
- Type GPedit.msc and hit Enter or OK to open Local Group Policy Editor.
Navigate to Local Computer Policy -> Computer Configuration -> Administrative Templates -> Windows Components -> Search.
- In the right pane, double click on policy named Allow Cortana.
- Select the Disabled radio button.
- Restart the PC and Cortana and Bing Search will be disabled. (May work after signing out and in again)

Source: https://superuser.com/questions/949569/can-i-completely-disable-cortana-on-windows-10