There isn't a whole lot to get right or wrong here. Bugs and other pests appear on screen, waiting to be shot. Some crawl around their little section of the on-screen circuit board, while others just sit there. If you don't shoot one in time, it disappears again. At the end of each wave, you are judged on your accuracy. Do well enough and you go on to the next wave of bugs. Miss too many shots and the game ends with one final rating of your performance.
If this sounds rather simple compared to other gun games like Nintendo's Hogan's Alley or even Duck Hunt, it is. The game is little more than a somewhat-animated whack-a-mole, only with a gun instead of a hammer. That wouldn't be so bad, except Bug Hunt suffers from the same problem that plagues just about every Atari gun game: terrible accuracy. So, what little the game strives to do, it doesn't. The result is immediate frustration, where there could have been at least a few minutes of entertainment. Skip this one and stick with the gun games offered by Nintendo and Sega.