In the UK, one disposes of unwanted stuff in the rubbish bin or merely the bin. The venerable U.S. equivalents are garbage can and trash can. In the April 18, 2011, edition of (yes) the New Yorker, one finds this in (American) Evan Osnos’s article about Chinese tourists in Europe:
He was a sanitation specialist by training, and he couldn’t help but notice Milan’s abundant graffiti and overstuffed trash bins.
notoneoffbritishisms.com 
I can see “bin” as perfectly fine in writing, but it could cause confusion in American speech, as many pronounce “been” the same way: responding to someone’s query about a bit of rubbish with the imperative, “Aw, just bin it!” could strike some ears oddly.
K, we’re guilty of that pronunciation too. Context rarely fails to deal with any potential confusion.
I think it works fine if you precede it with the adjective.
How about ‘bin’ as a verb? I’m okay with it, but I know some people go crazy at it. By the way, most of the locals here in Hong Kong have never even heard of ‘bin’ as a verb, and it makes for quite hilarious conversation sometimes when they hear it from expats and foreign-raised people.
“Bin”=”throw away” has probably never been used by an American, as of now.
In the U.S., I think “bin” is often used to describe larger, more ‘industrial-use’ containers, as in “recycle bin”. Here is one recent, sad occurance of “trash bin”: http://usnews.nbcnews.com/_news/2012/09/27/14124091-son-arrested-after-moms-body-found-in-bronx-trash-bin?lite
This reminds me of a joke [text in brackets is my attempt at US English translation]…
Dustbin man of Chinese origin: Where you bin?
Householder: On holiday, mate. To Spain.
Dustbin man: No, where you wheelie bin?
Householder: No, really, I have.
My attempts at US English translations:
Dustbin man = trashman
Holiday = vacation
Wheelie bin = trashcan (the kind on wheels that you put outside for your rubbish to be collected by the dustbin lorry [garbage truck]).
I’m going to guess that use of “bin” for both “trash can” and “throw in trash” have increased exponentially among Americans since this was posted. It seems like I hear it all the time from Americans.