The gerund is fine. You could use the infinitive but you'd have to put a noun after it like, "paper", "plastic" or even just, "rubbish". Alternatively you could bypass the gerund and the infinitive altogether and just say, 'we need to know if they use recycling bins.'

Use "for recycling". If you say "to recycle" it could mean that you want to recycle the bins instead of using them for recycling.