Hardly any bugs are out 'roudn this time of the year. Click herehere to fine out which ones.
Just remember that most insects run when you make too much noise or come too close. Be sure to walk slowly (You can hold A to walk slowly and sneak up on bugs with your net out).
Bugs are a pain to catch, especially the ones you have to dig up. After you dig them up they run even while your switching to your net in your inventory. I have lost 2 out of 3 bugs that way. So far I have 2 bugs, forget which ones. Both of them was dug up though.