Should part 1 be like- while he was crossing the road because of passive structure in part 2.
The question we have to answer is "Who was crossing the road?"
While crossing the road, the old man was hit by a bus. [The old man was crossing the road.]
While crossing the road, the bus hit the old man. [The bus was crossing the road. Presumably, the old man was just standing in the middle of the road, else the bus would not have hit him when it crossed the road.]
Of course, the second sentence is absurd. If a bus is crossing the road, clearly the bus driver should be fired.
Here is the point: the phrase "While crossing the road" is intended to modify "the old man"--that is why it appears in close proximity to him in the sentence. The passive voice is irrelevant.
In order to cast this as an active voice sentence, you could write something like:
The bus hit the old man as he was crossing the road.