Is it permissible to take a loan from an interest-based (ribawi) bank out of dire necessity, represented by the unavailability of transportation and exposure to danger, with no other alternatives available?

Necessity does not permit dealing in usury; rather, dire necessity permits it. Dire necessity is that which is highly likely to cause a person to perish, or endure unbearable hardship, or be unable to secure the minimum standard of living.

If you cannot find your livelihood except through work, and you found only the aforementioned work, and traveling to it by a private car is safe, but without it you would be exposed to real danger, then this situation falls under dire necessity. It is permissible to purchase the car through a usurious bank if you find no other way.

It must be noted that a woman is not permitted to travel except with her husband or a mahram, based on what was narrated from the Prophet, peace and blessings be upon him: "A woman should not travel except with a mahram."