Hi @hcedwards,
Welcome and thank you for posting on the Instructure Community!
Is your course associated with a paid canvas account? Meaning, does your institution pay for their own Canvas instance and your course is associated with it? If so, your student will not be able to sign up for the course with her own free for teacher canvas account, since they are two different canvas instances managed by two different admin teams. Unless associated with a trust account, which in this scenario isn't possible, you can't exactly access courses from other instances on another one that isn't associated with the same institution.
I recommend having her register for an account under the Canvas instance your course is associated with. If registration for student accounts isn't enabled for your school's institution, then one of your canvas admins will need to create an account for her.
However, if you're using free for teacher like she is, please ensure she has successfully signed up and has received the confirmation email. Upon that, ensure that your course is published and that you entered the correct email or login ID when inviting her to the course. She will then be able to sign in and accept the invitation with no problem.
Reach out with any additional questions or concerns, we're happy to help!
Good luck and all the best,
Noah