Running for the bus, the rain began to pour.
If you really think about, it's saying that the rain is running for the bus, which makes NO sense. Here, read it again...
<em>Running for the bus, the rain </em>began to pour.
The author wasn't specific about <em>who </em>exactly was running for the bus.
Not sure if it asks you to do this, but if you were to change it and make it agree, it would be "<u><em>As I was running for the bus</em></u><u>,</u> the rain began to pour." There're other ways to write it of course, but the point is that now you know who actually ran for the bus, and it makes sense.
