My Vos Ekkie "Angel" was similarly shy. She'd speak only in the absence of an audience. My male, "Sasquatch" was less reserved but preferred to speak alone.
Unfortunately many birds will speak when desired but not on command. Difficult to train with a reward if she won't perform in front of you.
Not so, good sir, easily trained!

Barbara heidenrich teaches this and works brilliantly for Parker. Simply come running with his most favorite treat in the world whenever he talks in another room.
He’s doing it for attention, it’s an attention getting device. He learns talking gets you to come back. When you return, no need to talk any more.
If you do come running to him making a huge excited fuss with food EVERY TIME he talks in another room, he starts realizing talking gets him not attention, but TREATS. This flip in mentality, speaking for treats, will start stoking him to talk in front of you.
Time may vary by individual but if your consistent with this for at least 2-3 weeks, you should notice a change at least within a week. It won’t be talking on your arm yet. It might be a whistle when you are in eyeshot but still 30 feet away. But he’s making mimics when he can still see you! It’s progress.
Key is consistency. You must have treats near you at all times (I popped popcorn and had bowls of it scattered throughout the house). And you have to react swiftly. When he speaks, From the other room start shouting “GOOD BOY!!!!” So he can hear the praise before you arrive in the room with a treat. Come RUNNING. I stubbed several toes in the process. He needs to see the fuss you make.
This is accelerated dramatically if you find a situation where they are likely to talk more, naturally. Parker gets his motor running when around running water. So dropping him on the shower rod in the bathroom with the shower water running, then walk out, will guarantee I get words from him. So I use that as a training session. Set him up in the shower, I wait just outside where he can’t see me, he talks, I come running with food.
I started this a year and a half ago. Parker does occasionally talk in front of my now. Not on command but he does sometimes say words while sitting on my arm or with me a couple feet away from him. He also now greets me almost every morning when I first walk into his room in the morning.
[ame="https://youtu.be/KVASr-NrIf0"]Morning salutations from Parker the parrot - YouTube[/ame]