Grasshopper

Cutting grass is the whole method. Swing through a patch of plain green grass and they pop out on their own, so you rarely have to go hunting. As bait they sit near the bottom of the pile, fine for the first few Angler quests and not much after that. Once worms or jungle bugs are available, retire them.

They move on the same code slimes use, which produces two odd results. They float instead of sinking in water, and they react to aggro the way an enemy does. Strip your aggro down and a grasshopper will hop toward you rather than flee, which makes netting one far less annoying than chasing a bunny around a hill.

A rare golden variant can turn up in place of an ordinary one, and it is worth far more than the grass you cut to find it, so keep a net on the hotbar while you are clearing plants for other reasons. Statue spawns cannot be caught at all; they vanish in smoke the moment you swing. A statue is scenery, not a bait farm.