It's only as my own mother has got old old that I have come to understand how ageing undermines people, particularly women. My mother is highly educated and was fiercely assertive on my behalf when I was younger, but I've watched her lose confidence and become more hesitant as her strength declines and, at every turn, the world tells her she doesn't matter and she tidies herself away and puts up with being treated as a waste of space, a relic from another era, an inconvenience. It was quite upsetting to notice that a lot of the time she just accepts.
My mother uses the internet, she's fine with routine tasks, but she's nothing like as comfortable with working out new things as she used to be. I do some of the searching legwork for her these days. She'd probably think to phone someone if she needed a lift to a hospital appointment, but I'm not sure she knows about patient transport.
If I couldn't take her, I'd do the research on other options, send her the links and tell her to call me if she needed me to sort something out. Because she isn't going to do that without an invitation unless she's desperate, because as an elderly woman, her experience is that the world finds her a minor inconvenience - until she needs help, when she becomes an irritating burden who has outstayed her welcome on this planet.
I should add that my mother wouldn't say any of this. She's still independent and probably more capable than most women her age, but she does sometimes need kindness or advocacy. I'm glad she lives somewhere where people are kind and that she has me at the end of a phone line.
OP, If you really don't have time to help at all, you don't and that's all there is to it. However my guess is that you are - in this instance - your neighbour's last resort. Not because she's cheeky or lazy, but because she just hasn't the mental agility - or perhaps lacks the confidence- to come up with a better strategy. If you could spare the time to point her in a better direction it would be a kindness. If you don't want this situation to crop up again it might be worth investing time in helping her towards a more robust source of help and advice so that next time you're not her first, last or only resort. Obviously it's sensible to be frank about this - tell her your help must be a one-off and she can't afford to be picky about whatever alternative you help to set up.
Sorry, long and probably pointless post, but seeing the change in my own mother since she entered her eighties has completely changed my perspective on incompetent old biddies.