It is permissible to pray anywhere when the prayer is due.
However, one must fulfill the conditions of prayer such as facing the Qibla. therefore, if a person is on a bus, he must face the Qibla, but if he is unable, then he can start his prayer facing the Qibla and then it is Ok to face anywhere else as long as this is not possible.
He also must pray standing up as this is a pillar of the prayer. if he is unable at all to stand –and this is hypothetical- he may pray sitting down.
If he is able to get off the bus, he should so that he can pray in the normal way.