What do you do about a friend who cannot make a request directly?

Q. I have a friend with multiple sclerosis. She lives alone in the countryside. There is no bus service and, due to her physical condition, she was disqualified from driving two years ago. I made my friend an open offer that should she need a lift, she should call me. Mostly I can oblige. But I failed to take account that my friend was raised never to make a direct request. Instead, if she needs a lift, she will manage the conversation until it is apparent that I should make the offer, which she will decline until, by a process of attrition, she accepts, sometimes with qualifications which mean I am not quite sure if I am to drive her or not. I should add that her MS is not the operative factor — she has always behaved this way.
I appreciate that a direct request has a certain indelicacy, but if the object of manners is to preserve the feelings of the other person so far as possible, there are surely situations when directness is the better option, if the alternative is to cause the other person to feel exasperated.