I am a school nurse in the greater Houston area. I am also a former teacher, and went to Lone Star to get my associates degree in nursing. My district does not require a BSN, but they do require two years of community health experience before they will hire you to be a school nurse.
It is not something that I would recommend straight out of school, since you only have yourself and your nursing knowledge to rely on in case of an emergency. I spent two years working for a pediatrician, doing telephone triage along with patient care, before transitioning to the school setting. I am so thankful for that experience, because I felt like I was trained to deal with most situations that I would encounter at school, as well as dealing with irate parents.
Your teaching background will be helpful in getting a school nurse position, since you are already familiar with the culture and "politics" of the school setting. The teachers at my school like that I can empathize with them, and that I don't keep students out of class unnecessarily.
Once you are in nursing school, you will likely do a clinical rotation in a public school, and you can see if it seems like the right fit for you. Good luck to you!