Cortana is fun. While she does mostly what I wanted on Windows Phone, I had some difficulties with her on my Surface Pro.
Mostly she opened only Bing when I wanted her to open an app, e.g. Groove Music.
Then I found the trick.
For some commands there should be no interruption or pause after “Hey Cortana”. If you wake her up with “Hey Cortana”, do not wait till it is written in the search box. Speak straight on.
“Hey Cortana” <pause a while> “open groove music” – this will open bing searching “open groove music”
“Hey Cortana open groove music” – without a pause it will open the app.