At that moment a bus arrived but, by the time my brother was helping the old lady back across the road, it was too late. The bus has gone.
It's not quite correct. The last clause is definitely wrong, and the middle one might be depending on the actual sequence of events:
but, by the time my brother was helping the old lady back across the road, it was too late.
Here we're saying that between the bus arriving and your brother helping the old lady (who presumably is known to the listener since we used the definite article) back across the road, it was too late to carry out whatever action you had intended on performing when the bus arrived (presumably boarding it).
Note that this is only correct if your brother was still in the process of helping the old lady when the next thing happened, that is to say they had not yet reached the other side. If your brother had completed the action when the bus left, you would instead say
but, by the time my brother had helped the old lady back across the road, it was too late.
We then come to your final clause, which should be
The bus had gone.
The reason we don't say "the bus has gone" is that this marks the present as the time reference for the sentence, but we're talking about an event that happened in the past, so we have to use "had" instead of "has". As StoneyB pointed out in the comments, you were using the present perfect instead of the past perfect.
In short, the answer to your question is "yes" but what you wrote is slightly incorrect.
The bus has gone.
The sentence is not in the past perfect; it's in the present perfect. The use of the past perfect "The bus had gone" is correct. So the correct statement is:
At that time a bus arrived, but by the time my brother helped the old lady back across the road, it was too late. The bus had gone.