if it is still available (i thought it was leaving for the beginning of november in nothern hem, that's why i rushed to try and get one myself before october finished), then i'm going to tell you the exact things i did.
you wont come across a stick bug easily, but you may have and just startled it. they're extremely sensitive to movement, so you need to have a clear visible view of your tree trunks in order to tell it's there, and get your net ready and waiting before approaching it. i had to catch a few bugs in the area i was trying to make it spawn; by catching the butterflies and grasshoppers that were around, i tried to make my game spawn in more bugs. i did this specifically around a lot of trees in hopes of getting a stick bug on one of them.
it also has to be between 4 AM-8 AM or 5 PM-7 PM for the stick to even spawn.