OP, I went straight into school nursing 1 year ago right after I passed the NCLEX and haven't looked back. I love it! However, being certified or credentialed can depend on the school and really, the best foot into the door is subbing. More schools, even public ones, don't require certification to sub, but again, it can differ widely between states and districts.
I work at a public charter school and I am working on my school nursing licensure, but not having it did not stop me from getting the job. However, a public school in my neck of the woods (MA), they want the licensure first, which requires a BSN and 2 years as a school, pediatric, or community nurse (and a test/coursework, etc). Private schools usually do their own thing, but again it can vary.
The CA School Nurses Organization should offer some more insight: CSNO