Traffic accident I saw yesterday

Yesterday, as I was crossing one of the nearby crosswalks, when I heard a loud bang and saw a bus stopping right after it had crossed moved across the center of of the Isu station(subway line 7 of in Seoul), I was crossing one of the crosswalk nearby.
So, I looked at the center of the crosswalk. There was a fallen motorcycle fell down and a biker lying down very close by.
Since it happened only a couple of seconds after the traffic signal changed, it is probably because the biker wanted to move fast before the bus arrived at the center of the crosswalk and violated a traffic sign rule.

In the first sentence ("Yesterday, as I was...") I have switched the order of your phrases. This is not technically a hard and fast English rule, but in English, we tend to put the context first (i.e., "I was crossing one of the nearby crosswalks") followed by the interrupting action in the preterite (i.e., "I heard a loud bang and saw..."). It just makes more logical sense when recounting a story!