I don't think that either OP or the other woman are at fault here.
OP, you have no obligation to continue to drive her, and you don't have to give a reason - just 'It's notgoing to be possible in future' - if she presses, then simply reiterating that you have other committments / need greater flexibility is fine, or simply saying "Some of the circumstances have changes, so it just doesn't work for me any more' is nice and vague but doesn't blame her.
Given that it is a long standing arragnmetn, I am with those who suggest giving her a reasonable period of notice - maybe 2-3 weeks. Then be firm.
If it were me, I might actually do arrange something for the first day (i.e. arrange to meet a friend for coffee after work, book an appointment with the hairdresser or even just plan to go to the supermarket on the way home, so that if you do get asked if you can help out 'just this once' you can stiffen your spine and explain that no, you have a prior committment which you can't cahnge (and no, it won't work if she offers to wait for you. You're going in a different direction / meeti g a 3rd party) I syuggest this not because I think you 'ought' to have a reason, but because it sounds as though it is difficult for you to say 'no', and you may find it easier to stick to if you have in your own mind a clear reason!
I don't think the other woman is a SS (based on what OP has said) - she has been a good passenger, she has perhaps been rather obtuse in relation to the changed hours etc but that may be that she is genuinely trying to be accommodating, not that she is deliberately ignoring hints.
And if any co-workers stick their noses in then I think the suggestion of PPs to turn it around and suggest that they offer is perfect.