Spoiler Alert
I think the key to making bugs appear is having a pet. I noticed early on that if you try to make the cat or dog come inside during a storm, they head into the bushes in the left back corner for the cat and the right back corner for the dog. I've played several experimental families where I didn't get a pet because they are always annoyingly under foot. In those families I almost never got bugs. So I've started a couple of experimental families where I have a pet, and I've noticed that if you chase the dog into the bushes during rain, you get leaves and twigs and an occasional bug. If you chase a cat into the bushes during a storm, you get bugs. You won't necessarily get a rare one every time, but you will get bugs.
I've also noticed that if you really keep on top of looking for collectibles when you first start a game, you can get over half of them in the first hour or so of play. I started one this morning where I had 27 collectibles after the first hour. Also, they don't have to take the collectible all the way to the chest or the computer, if you pick it up and drop it, it goes where it is supposed to go, and you get credit for it. That speeds things up so that you can get a bunch of collectibles while you are pulling weeds and cleaning up the house, even with only one person. And lastly, pulling weeds seems to stimulate the appearance of coins, particularly in rain. All of these make sense, as disturbing bushes (cat and dog) will scare bugs out or make twigs, leaves and nuts fall, and disturbing soil, especially during rain, turns artifacts out of it, like arrowheads and coins, in real life. It looks like LDW programmed real life scenarios into the game.
Also, some of the bugs are really hard to see and easy to miss. The grasshopper is almost invisible in the grass. I've found the dragonfly once on the hose in the backyard, and it was transparent and almost invisible on the hose.