He's referring to the container, though, rather than what I would call 'the rubbish'.Even in the southern United States, where I live, we would recognize "dustbin" just fine even though we usually just refer to it as "the trash" or "the garbage".
An American might figure out what you meant by "dustbin" (although I am not nearly as sanguine about that as is Bildsturmer), but few of my compatriots would understanding your meaning if you asked where the nearest bin was. You would instead be far more likely to be shown where the household stores its flour.Yes, that's fine. I'd probably just say bin rather than dustbin.
I disagree again with Bildsturmer. You do need to say that (or an equivalent, such as garbage can) if you actually want to find a container, rather than a possibly uncontained heap.Ah, you needn't say trash can. Thanks for that.