Q: I've taught in the private sector for years and want to move into K–12. How can I do it?
A: Most public-school systems require a certification or license to be on faculty. If you'd like to work in the public-school system but don't have the necessary license, you can become a teaching artist at a school. This means you are booked to teach for a specified duration as a specialist. I can attest to this being a good way to begin—it's how I got my start.
In New York City there are arts education organizations that contract with public schools to provide residencies for teaching artists. These organizations are cleared by the Department of Education and vet artists for the schools. If you don't have these in your area, you'll need to look into other ways to approach your school system. This could be as easy as reaching out to administrations to see if they have some discretionary funds for special projects.
If this is a long-term career focus for you, I would recommend taking some courses on pedagogy. A master's degree in dance education would certainly prepare you to pass the exams required for your teaching certification, but there are other professional development opportunities to get you started before fully committing. The Dance Education Laboratory of the 92nd Street Y in New York City (where I teach) has great programs both during the year and in the summer. Luna Dance Institute in Berkeley, California, is a good option for West Coast teachers, or if you want to learn online, I recommend the NDEO Online Professional Development Institute.