Is it obligatory for me to quit my studies despite my father's objection, due to mixing on the bus and the embarrassing content of the study material?

If the female student can complete her university studies while adhering to Islamic regulations, such as providing safe transportation, avoiding forbidden lectures, and observing Islamic dress codes ( Shar'i hijab), then that is better, as it involves obeying the father. However, if she cannot avoid prohibited acts or fears temptation, she must abandon her studies, as there is no obedience to a creature in disobedience to the Creator.