The important part is that there is no way to know if women really will choose a private vehicle over the bus. We have examples all over the world of women who could drive if they wanted to (they could get a license and afford a car), but they don't. Is this a small minority or not we really cannot say.

Given same price is false - a car is always more expensive, but many of the costs of a car are fixed, gas itself is cheap while you still have to make the car payment even if you ride the bus and let the car sit - so it seems like a car could be cheaper.

I believe that given transit is a reasonable option for most trips (not just getting to work) most women will decide over 5 years that transit is safe and will start using it. However there is no real way to know except to try it meaning your bet is not really possible - there are too many variables allowing me to say you didn't do enough.