All above advise is great. I advise going into your local school district office and asking about becoming a school nurse substitute for your district. If your law requires a school nurse in every building, like Delaware, subs are a must. Also check the websites for each school district that is close enough for you to drive to and look at their job openings.
You get to know if you really like school nursing that way, and get to know fellow school nurses who can fill you in on job openings. In our tiny state, all the school nurses get together 3 times a year for dinners and conferences/meetings. You get to know whose retiring and leaving also, so you can fight for their job :P I went to these dinners as a sub, they dont care as long as you pay and as a sub- you are very much valued by the school nurses!
In some states, school nurses work through the public health department. Other states, school nurses work for the schools themselves and are hired and paid by the state that way. And school nurses also work through local hospitals and are hired and paid by them.
So its worth finding out how school nurses work, through who, in your state so you know where to look for job openings.
Good luck!