What does the Bashful nature do?

Bashful is a neutral nature. It does not raise or lower any stat.

Can I change a Pokémon to Bashful?

Yes. Use a Bashful Mint to apply the Bashful stat effect to any Pokémon without changing its displayed nature.

Nature

Neutral: no stat is raised or lowered.

No stat is raised or lowered.

Filler nature; sometimes used on mixed attackers to avoid lowering any offense.

What does the Bashful nature do?: Bashful is a neutral nature. It does not raise or lower any stat.
Can I change a Pokémon to Bashful?: Yes. Use a Bashful Mint to apply the Bashful stat effect to any Pokémon without changing its displayed nature.