Is it permissible for a woman to ride a bus or a taxi alone or with her Muslim neighbor for shopping and recreation, especially if the driver is non-Muslim?

There is no religious impediment for a Muslim woman to ride a public transportation bus within the city, as long as there is no khalwah (private seclusion with a non-mahram), suspicion, or travel involved. It is permissible for two women to ride with the driver if there is no fear of fitnah (temptation or discord). However, if there is no one else in the bus or car besides the driver, it is not permissible for a single woman to ride with him if he is a man, based on the Prophet's (peace be upon him) saying: "No man should be alone with a woman unless a mahram is present." Similarly, if it involves travel, she is not permitted to travel except with a mahram.