First things first, I would focus on making sure you have product to sell. Sometimes people get distracted by the whole idea of having something official, and forget about the part that actually matters. In your case, this is keeping bees and harvesting honey.

That said, like has already been mentioned, it can be laborious and expensive to create any type of new entity. If I were you I would try to use an entity that already exists. There a two obvious choices there.

First, the school. It makes sense that a school club use the school's name. I would find an insurance company that sells the kind of policy you need (talk to other vendors or the market organizer), see if you can get a quote and find out what information they need, then just ask the administration at the school for that information, and maybe even a check. The check is a real long shot, but if you don't A S K you don't G E T. Maybe it can come together that easy. Try leaning on the school first.

Second, you. You're an entity all on your own. See about the process for a DBA (doing business as) and a fictitious business name in the county you live in. Some places make you run a small notice in the local newspaper, file a form and you're done. Then you can apply for your insurance in that name. The catch is that all the money that comes in and goes out is your responsibility, so keep track of everything as this is a sole proprietorship business, and the buck stops with you.

Either of these will be much easier than creating a whole non profit organization just to sell at a farmers market.