Bidoofs 1-16 is what Rusty refers to the pile of sixteen Bidoofs that he tried to capture inside one pokeball.
It is actually made up of sixteen different Bidoofs, all pressed together in one pile. Four of its heads are visible along with two bodies and a couple hands and legs.
It is first seen when Team Rocket first attacks Rusty and searches through his pokemon. Rusty claims that he had to "catch 'em all," and since he ran out of balls, he had to reuse one, resulting in a bloody mass of the Pokémon. Bidoofs 1-16 were presumeably left behind when Rusty's Dad came and picked him up.
It is next seen as a ghost, haunting Rusty in the Pokemon Tower. They call him a murderer and yells at him that "one Pokémon per Poké Ball, that's how it works!" It then tries to kill him along with his other deceased pokemon before Grandpa Crispen intercedes. He then flees when Rusty captures his grandpa.
In Bidocalypse, Bidoofs 1-16 was most likely to die again due to Future Rusty's repeated actions.