Do the honors yourself.
For starters, we can't send invitations to people via Socratic yet, so you're going to have to tell her about us yourself.
That said, even if we had the option to send invitations, a personal note from you would probably work best, especially since you know her.
So don't hesitate to let your teacher know about Socratic, I'm sure she'll love it here! :D
In fact, you can even mentor her on how to post answers, add images, or use the math formatting and show her around, we'll be happy to welcome her to our community!