What is better to do while riding the bus when hearing the Quran or songs: listening to the Quran, or reciting adhkar (remembrance of Allah) and the daily Qur'anic portion, or studying worldly sciences?

If there is a recording of the Qur’an playing, the priority is to listen attentively, unless there is a time-bound dhikr (remembrance of Allah) that would expire, in which case it would be better to engage in that dhikr. Listening attentively to the Qur’an is recommended and is not obligatory except during prayer or a sermon. There is no harm in reciting the Qur’an and remembering Allah silently when the driver is playing music, and playing music does not imply preferring the study of worldly sciences over reciting the Qur’an and remembering Allah.