Is it possible to see whether you are within a ~10m radius of another phone without broadcasting location data?

I was looking at Bump_(application) , and I found it interesting that they use location data along with other metrics to figure out whether two phones are next to each other. Is it not possible to do a similar thing using bluetooth or a similar technology that doesn't send your location data to a remote server? I'm assuming the two phones in question have the same app.