Hear hear, Phil! I agree. Recycling bin, it is! A bin for the recycling. A recycled bin would be a bin that has been recycled. A recycle bin ..is...er... dunno. Well, it's obviously a recycl-ING bin without the -ING.

I think you are absolutely correct, Yu Gong. Perhaps they started using the shorter "recycle" as a way of saving screen space. In any event, you will often hear "recycle bin" in reference to the virtual kind on your computer desktop. For a real (i.e. not virtual) one, I would say "recycling bin".

‘Recycle bin’ sounds natural because it is part of a group: trash bin, yard waste bin, garbage bin. So technically you could call it the ‘recyclable materials bin’ but ‘recycle bin’ is perfectly clear and much shorter. ‘Recycling’ doesn’t sound wrong, though, because we do use the word ‘recycling’ to mean ‘recyclable materials’. Without the word ‘bin’ attached, for example, it’s natural to say: Put that in (the) recycling. I.e. ‘recycling’ has become a noun which has a specific meaning - it’s relation to the verb ‘recycle’ is more distant. If you compare words like ‘washing machine’ or ‘ironing board’, they are much closer to the verb. We are actually washing and ironing the clothes. But we aren’t actually recycling anything when we put it in the bin. Someone else will do that - we’re just classifying the waste.

By adding -ing you are forming a gerund, so that the action functions as a noun. Anexample would be any form of activity you enjoy doing. Instead of saying "I like to fish" to imply the action, you can just say "I like fishing", which arguably sounds more natural.