According to Kikar, Rav Yitzchak Zilbershtein, rav of Ramat Elchonon neighborhood of Bnei Braq, was recently asked a detailed question about a woman driving. An avreich asked specifically about his wife being able to drive. Knowing that it is a tzniyus problem, can she drive because the alternatives are worse, or at least no better?

The avreich detailed that his wife needs to travel a half an hour each way to get to work and back home. In addition, she has errands to run and other things to do that she needs to go places for. So, on the one hand she can drive and get there quickly and  do what she needs to do, despite the tzniyus problem of her driving. On the other hand, there are alternatives, none of which are very good with tzniyus problems that are worse than when she drives her own car:
1. she could take a bus. This too has tzniyus problems as there is no mechitza and men and women are mixed and the bus is sometimes crowded, and the drivers are often not Torah-observant people.
2. She could take a taxi. This too is problematic, as most of the drivers are not Torah-observant. And, even with a frum drivers, it is a situation of a private car ride with a man and a woman secluded together. It is at least quasi-yichud.
3. she could walk. This [resents a problem with long distances and both the ability to walk them and the amount of time it would take, but it is also a tzniyus problem as she is exposed for other strange men to look at her while in the street.

The avreich concluded hsi question by saying that the option of her driving a car seems to be the best (or, least bad) of them all.

So, can she drive a car?

Rav Zilbershtein responded saying that her driving is actually the worst of all the options. bus, taxi and walking present problems, but she could be careful to not cause men to stumble. There is, however, no intrinsic problem with tzniyus with any of these options. Driving a car, however, is completely against the rules of tzniyus for a woman.

Besides for the various problems it causes and for her need to be in contact with men, it is actually prohibited for her to drive. Rav Zilbershtein explained a verse in "tefillas haderech" in which we pray for a safe trip that says "says me from dangerous animals on the way". He explained that this also refers to drivers who do not follow the rules  of the road, and they turn the situation on the road to one of war, and war is not for women.

Honestly, to me, that seems to be a real stretch. Like shooting an arrow and then drawing the target around the arrow after it hit.

But, to go on.. Rav Zilbershtein relates a story of a woman who was driving, a very important woman very involved in chessed, and she drove into a tree and became handicapped for the rest of her life. Rav Yechezkal aAbramsky had said about that case that it was because she was driving, and a woman should not.

He was not just saying that women are bad drivers, but he says there is a spiritual problem caused by it that results in such accidents. It causes terrible pritzus, is opposed to the concept of "kol kvoda bat melech pnima"...

Rav Zilbershtein went on to blame (at least as one of the factors) the high rate of traffic accidents on Israeli roads, in which many good people have been killed, on women driving cars  - again, from a spiritual perspective. In addition to the spiritual problems, he adds that women cannot deal with the high pressure situations and sometimes cause these accidents.

The only way a woman could drive, according to Rav Zilbershtein, is in a situation of great need, such as a woman who must take her handicapped child for treatments, and other similarly unique and extreme situations and then a specific question must be asked to a rav. Rav Zilbershtein also adds that driving abroad might be a different situation and rabbonim there should be asked when relevant.

I dont know when Rav Abramsky said what he said, but he died over 40 years ago, so it was definitely not so recently. Being that it is so common nowadays for women to drive, I wonder how it could really still be considered such a serious tzniyus and spiritual problem - not including certain extreme elements that still consider it so - elements I was not aware Rav Zilbershtein is associated with. Far be it from me to argue with Rav Zilbershtein, but I do wonder about that.

Pointing to one case of a woman driving and getting into a bad accident is nothing but anecdotal. Many men and women, unfortunately, get into bad accidents. Crazy drivers can be found among both men and women, as can their victims.

In the original question asked, I am not sure what the relevance is in pointing out the lack of Torah-observance of the bus drivers. The taxi driver's observance is understandably more relevant, as the driver would be alone in the car with the wife. A bus driver is driving a bus filled with many people, so I wonder what relevance his level of observance has.