There are lots of bugs everywhere. Collecting them is encouraged, but I don’t see a use in them. They aren’t needed in crafting or sellable to the peddler at night like materials, it seems. I’m obviously still gonna collect them all, but why am I doing it?
You could use the bugs you find to infuse the potions you buy to become more useful in your adventures or sell excess bugs to Strich in his room at the Academy at night.
To infuse your potions, you first need a bottle full of a potion purchased from Luv, the Potion Shop lady at the Bazaar. Next, take your potion to Bertie, her husband that’s holding the baby to get your potions infused. He will tell you what bugs are needed to infuse your potions and how much rupees it will cost.
You could also sell them to Strich, the tall bug guy who is/was one of Groose’s lackeys. If you visit his room in the academy at night (the one closest to the lower entrance), he will offer to buy some bugs from you. He will only offer to buy three types of bugs at any one night. So if he’s not interested in buying ones you want to sell, come back another night and hopefully he will be interested then.