The short answer is, it depends. Yeah, I know, not the most definitive answer, but hear me out. If you're planning to eat your pumpkin bars within a day or two, you're probably fine to just leave them out at room temperature. But, if you're planning to store them for longer than that, you're going to want to think about refrigeration.
Think of it like this: pumpkin bars are like a delicate flower, they're sensitive to temperature and humidity, and can wilt quickly if not stored properly. So, if you're planning to store them for an extended period, you'll want to make sure they're in a cool, dry place, like the fridge. This will help keep them fresh for longer, and prevent them from growing bacteria.