Hard to tell what might have led to this aside from the driver's inattention, but....do you think she would have hit you if were a pedestrian?- and if not, why not? Food for thought.
My suggestion would be for you to not cross the crosswalk if there is a car coming. Assume they are not going to stop. Assume they don't see you and are not paying attention. Wait until either the car has completely stopped for you or until there is no car approaching within hitting distance of you at all.
It is frustrating when bikers have the right of way but are hit anyway, but if we ride as though they are not seeing us and as though they are going to do the wrong thing, then we greatly increase our chance of survival. The fact is that it's very common for drivers to not see a bike in plain sight- simply because they are not LOOKING for a bike.
I'm so glad you didn't get badly hurt.
Watch those crosswalks- they are highly dangerous places for bikes.