She didn't want to be considered a trainer, I guess? Especially not with a pokemon that knows pretty much no moves.
That being said, that's a bullshit excuse, and about 3/4 of the plot wouldn't have happened if she'd shoved Nebby into a pokeball.
Alternately, Nebby in its first form broke out of every ball thrown, so she just shoved it into her bag instead. But considering that she most likely had access to a Master Ball, that's also bullshit.
