This is Mary's issue to handle.
You're in an area where taking public transit is a normal part of life and would be considered a standard life skill - it's not like you're expecting someone to instantly go from a small isolated village in the Arctic to navigating the Tokyo transit system in one step. She's taken the train before on multiple occasions, just not by herself. And re-arranging things so that you can escort her home involves a considerable inconvenience on your part. So it would be better to reschedule to a time when it's easier to do.
In the general sense - it's the prerogative of any person to decide that that they don't want to learn to do something - it makes them uncomfortable, or they aren't interested, or they find it too complicated, or it's not worth the effort to learn. But it's also their responsibility to figure out a way to handle their lack of knowledge or skill.
Take taxes - deciding that doing your taxes is too complicated or too much work is pretty normal. But if someone doesn't want to learn how to do it, they hire an expert to do it for them (or in some cases, they turn it over to their spouse). They don't go to random friends and demand that they do their tax return, or simply not file claiming it's too complicated. (And for that matter, if you have a complicated financial life or aren't very good at reading legal/financial documents doing your taxes yourself can be a big mistake).
Things change when there is an external reason why someone can't do something, but it still doesn't put the responsibility totally on other people to accommodate. So if Mary has a diagnosed anxiety disorder that means that she is fine on the train with an escort, but panics when she's alone, her friends are likely to be more accommodating. But in the situation described by the OP, it is still probably better to reschedule, because the OP is not available to do the accommodating.
I think some of the individual variation comes from temperament, and some from experience. If you have a life that doesn't tend push you out of your comfort zone - you have your job and your friends and your routines, and there is little upset or sudden changes - it can be easy to avoid learning new, scary things, and you can keep this up for years, which makes it even harder to push yourself into something new.
On the other hand, if your life pushes you into new situations, voluntarily or not, you have to adapt or you lose the ability to function. If you move to a job in a big city where parking and taxis are horribly expensive, then you learn to use public transit or you stay home and lose your job. One of the most striking examples of this is what happens when someone's spouse dies or divorces them after a long marriage. Suddenly, the widow or widower is shoved into having to do things that their spouse always took care of - driving, doing taxes, arranging for home repairs, cooking, buying clothing, organizing a social life. And it's often a massive, painful adjustment, but something that has to be done.