When Bard kills Smaug, he does so with his special black arrow which never failed him before. He also says it was from his grandfather. After all, Dale and Laketown are connected, and Bard is a descendant of Girion of Dale. Here is the relevant text from the Hobbit:
'Arrow!' said the bowman [Bard]. 'Black Arrow! I have saved you to the last. You have never failed me and always I have recovered you. I had you from my father and he from of old. If ever you came from the forges of the true king under the Mountain, go now and speed well!'
Since dragons somehow know a lot of things, he probably knew that Bard was a descendant of Girion.