A pokémon breeder is primarily a Pokémon Trainer who raises and mates carefully selected Pokémon to reproduce specific improvements in future generations of Pokémon, such as moves, individual values, or natures.

In the games, they can often be found near Pokémon Day Cares. They raise a large number of varied Pokémon, generally maintaining a balanced team, although they are often weak compared to other trainers in the area they reside in.

In the anime, breeders typically concern themselves with raising Pokémon for health and happiness, rather than for Pokémon battles. They also participate in beauty contests and related competitions—not to be confused with Pokémon Contests, though it is common for them to take interest in these as well.

Aspects of Pokémon breeders in the anime typically also handle or cover include:
Monitoring, taking care of, and hatching Pokémon eggs
Pokémon grooming
Pokémon nutrition
The first, however, is mostly based on assumption. Breeders in the anime have not been seen helping Pokémon breed.

-Definition from Bulbapedia

I don't think Belle would make a good Pokemon breeder, she's too nice!