Cortana does control MusicBee on Win10, but it is rudimentary.
How I did it:
I associated MusicBee with all the music-related file types.
Then I made sure that Cortana was working.
Then I just said, "Hey Cortana, play some music."
She then opened MusicBee, selected three albums, shuffled them into the Now Playing playlist, and started playing them.
Cortana responds to "Next Track", "Previous Track", and "Pause".
In MusicBee, she does not respond to "Resume" for me, unfortunately. If you say "Play", she selects new albums and starts playing.
On my Lumia 925 phone, I can say, "Hey Cortana, play Led Zepplin" or "Play Jazz music" and she will.
But it does not work on Win10 with MusicBee.
It will work with Win10 and Groove though.
So Cortana works with MusicBee in Win10, but it is pretty basic.