From Bulbapedia, the community-driven Pokémon encyclopedia.

A Bug Catcher (Japanese: むしとりしょうねん Bug Catcher Boy) is a type of Pokémon trainer that first debuted in the Generation I games. They are generally depicted as little boys in hats and carrying nets.

They specialize in weak Bug-type Pokémon.

Experienced Bug Catchers apparently become Bug Maniacs.

Bug Catchers also seems to exist in the anime, since Ash Ketchum has been seen to have the net of a Bug Catcher.

Appearance

Bug Catcher Sprites

Image from Pokémon Red and Blue

Image from Pokémon Gold and Silver

Image from Pokémon Ruby and Sapphire

Image from Pokémon FireRed and LeafGreen

Image from Pokémon Diamond and Pearl

Generation I-introduced trainer classes
Beauty | Biker | Bird Keeper | Black Belt | Boss | Bug Catcher | Burglar | Champion | Channeler | Cooltrainer Cue Ball | Elite Four | Engineer | Fisherman | Gambler | Gentleman | Hiker | Jr. Trainer♂ | Jr. Trainer♀ | Juggler Lass | Leader | PokéManiac | Trainer | Psychic | Rival | Rocker | Rocket | Sailor | Scientist Super Nerd | Swimmer | Tamer | Youngster
Beta classes
Chief | Pokémon Prof.