If your bouncy unit is used on school grounds, and your group is under the umbrella of the school, surely the school is liable.
If you are independent, non 501c3, as we are, the liability may still fall to the school, it does for us anyway.
Your best bet is to contact your superintendent and get advice from her/the district lawyers about their policies and insurance coverages and what if any, liablity your group would be bound to.
OOPS>>>>>We just purchased one, the big water slide from Walmart and we planned to purchase several regular jump house types because we were renting them every year from a local rental place. We never asked the BOE about it. Dosen't the PTO Insurance that we have for the year cover us for any accidents???
The important safety issues here are that someone would have to be able to supervise the children on the bouncer at all times and there is a certain # (I think 5) of children they reccomend only being able to use it at one time.
I can't really give you ammunition, but I can tell you that this would need BOE approval for your group to even think about doing it. So I suggest you take the info you have to a BOE meeting and see if you can get their blessing on doing this. If the BOE is agreeable then take it back to your group for discussion.