To catch 100% of the bugs, hit ALT as soon as the bug appears, move your net to the right of the bug, and swing your net. ALT freezes the screen. If you do not have the net in hand, pick up the net then quickly hit ALT again (picking up the net unfreezes the screen) then move to the right of the bug and swing.
Several of the bugs require certain plants to be growing. Some are the bamboo spider, cactus spider, tahitian spider, etc. (The golden spider requires the ridgeball to be growing)