My daughter went through this. It was at its peak when she was 3, and it started because an insect landed on her at the park. She never wanted to go to that park again that summer, but the bug fears did die down after the first month of spring's extra-buggy conditions. I thought she was over it, but then when the bugs hatched again in the spring when she was 4, her fears kicked up again. She didn't even want to play outside. Now she's 5, spring is here, and she has talked a lot about insects--asks lots of questions about spiders and flies and bees, do they sting, where do they come from, how she wishes they weren't here--but she's not been hysterical about them like she has been the past two years. I don't think she's ever going to be one of these kids that is willing to hold the giant hissing Madagascar crickets at the science fair, but she definitely has outgrown her hysteria about insects--just as she outgrew her hysteria about monkeys and trains and garbage trucks.
And as much as I appreciated everyone's good intentions and advice, NOTHING made her more comfortable around bugs. If there were bugs at the park, we had to leave. If there were teeny fruit flies in the backyard, we had to come indoors. It felt very limiting, especially when I looked ahead and imagined an entire summer spent indoors nursing this child's irrational fears. But, really, it lessened as the bug population evened out, and especially as she grew up and got more verbal about expressing her trepidation about bugs.