Use gameHasControl to check for other BAP using music:
bool gameHasControl = Microsoft.Xna.Framework.Media.MediaPlayer.GameHasControl;
if (!gameHasControl)
{
MessageBox.Show("stopping other player"); // normally you should ask if to do that
BackgroundAudioPlayer.Instance.Stop();
}
Once it is Stopped, when you start your BAP, then old instance invokes Shutdown(), and your BAP will be new Instance, which you can normally use. The same is when your BAP is in memory and you start to play from Music+Video Hub.
Only watch out, because when you use XNA, you sometimes need to do:
FrameworkDispatcher.Update();
Otherwise your App will sometimes crash. Good luck.
EDIT - after comment
To make it work you need to add a reference to Microsoft.Phone.BackgroundAudio or use like this:
Microsoft.Phone.BackgroundAudio.BackgroundAudioPlayer.Instance.Stop();
BackgroundAudioPlayer is a Singleton
which you are allowed to use - in this case - Stop it playing (of course give the choice to the User).