How old are the kids? If they are old enough to be participating without parent interaction, I'd put out some snacks for adults during bounce time. Then I'd provide each child with a drink, slice of pizza, serving of veggies and piece of cake. I'd have one extra pizza just in case but I agree that adults don't tend to eat at those types of parties. If anyone is still hungry, they can make dinner at home afterwards.
This might not be the case with all bouncy places, but the 2 local places in our town (one independent, one is a franchise) don't allow you to have anything besides pizza, cake, and drinks. You also aren't guaranteed to have access to your party room before the food is served if they are having lots of parties that day. Kind of a pain, but they really run these places like clockwork and the upside is there is very little planning or prep for the host parents to do.