Louis Pastuer discovered that the source of the disease was the fleas, often found on rats. Therefore, the transmission of the Bubonic Plague was from fleas to humans.
I can't remember the exact title of the book, something about "ports" and "plague" but it's a good read, and detailed the third pandemic, which arose in China, in the 1890's. Credited with isolating the bacterium were Alexandre Yersin of France, and Shibasaburo Kitasato of Japan. Much of the book I read online.
For many years (a few generations) Kitasato was given the bulk of the credit, but as it was later found that he did not in fact "isolate" the bacterium enough (there were other bacteria present), the credit was given to Yersin.
From the lazy, non-bookmarked/lost all old bookmarks man's reference guide http://en.wikipedia.org/wiki/Bubonic_plague