I got fed up with plastic wrap like this when I was a teenager, only ever bought sandwich bags after that, and continue to do so. They have rather large ones that are capable of storing the whole bowl and then you can just usually tie off the end to make it air tight. And you can double bag as well, just in case you know it's going to make a mess.
Sandwich baggies are made from the same material as plastic wrap, and I get them in packs of a thousand. Only one is needed to store a whole half of a loaf. But I buy large bread loafs. But their main use case is to store bowls, dishes, containers, in plastic wrap. Useful when the deli meats have non re-useable sealed tops, just put the whole plastic tray they came in inside of the sandwich baggie. And tie it off.