What is the ruling on a wife going with a driver alone to the university if no mahram is available to take her, and she cannot find a female companion, and she is of good character and does not speak to the driver?

It is not permissible for a woman to be alone with a foreign driver because it is considered an unlawful khalwa (definition) (private seclusion). The argument that this is not khalwa as long as it is within the city or in front of people's eyes is a weak argument, because the most important dangers associated with khalwa are anticipated between those who are alone in the car. It is advised to protect one's wife and to transport her oneself, or for her mother or some of her sisters to accompany her, or to find some female students to accompany her.