We just call them bins in the UK, not trash bins. Putting something in the bin idiomatically means throwing it away. Perhaps that's a modern usage. We do also have bread bins, which is about the only use meaning 'receptacle' I can think of outside of warehouse bins.
I think it is a UK phrase, or at least not US. A friend of mine from Taiwan, with excellent (US) English, had never heard of using the word 'bin' for trash before.
It's not common in the US, but you hear it now and again here. The most similar example I can think of is probably "lift." You'll hear someone call an elevator that every so often in the US, but it's mainly the UK term
