The best “bait” for caterpillars is a patch of their host plants. The target here is egg-laying females, of course. Very few caterpillars wander and it’s mostly female choice where to lay her eggs that determines where they spend most of their larval time. A patch of host plants will give off more of the scent signals the females are searching for than an isolated plant.
Once you have identified likely host plants, I find the best ways to find the caterpillars on them is to look for feeding damage and frass (droppings) on the plants. Caterpillars need to eat a lot and create tell-tale holes and markings on the leaves they chew on. Some have special modes of feeding - e.g. larger monarch caterpillars will often chew the petiole until the leaf droops down, so looking for those drooping leaves in a patch of milkweed can help with finding them.
Caterpillars are also themselves food for a lot of predators, so they tend to either camouflage or hide themselves really well. Many of them will be out of sight on the underside of leaves, and inside curled-up leaves was already mentioned as another strategy. However, they do need to poop a lot with all the eating they do and they are piggy little worms that just ooze their droppings all over the place. If you see caterpillar frass on leaves or the ground, check the underside of the leaves above the spot. I have found quite a few caterpillars by searching around on the plant after finding their droppings first.
Similarly, beetles may be attracted to particular food plants. The Japanese beetles in my yard for example always seem to congregate in large groups on evening primrose to mate and defoliate the plants while they’re there. Not always is the plant the food - I can usually find all life cycle stages of lady beetles by looking for aphids/ants on plants around the yard.
Some will emerge just for a short time of the year, so knowing when and where to look for them can pay off. There are some big beetles around my yard that seems to only fly during about two weeks in the summer and only in the areas with taller grasses. These seem to be active during late morning to early afternoon, while others fly in the evening or at night. I find leaving my porch light on during late spring and early summer evenings will attract a lot of beetles, especially the large June bugs.