Well, I'm going to disagree with just about everybody else. I would say yes, go ahead and help, but the way you do it is key.
In your shoes I would tell the woman you're working with that someone who wants to remain anonymous has suggested that she would like to help out a client by paying a bill and that you would like to nominate this lady. Then you can make arrangements to pay the bill without handing over any cash at all. I do this frequently in a number of situations and all you need are the recipient company's bank details and a name, address and reference number for the account being paid.
Doing it this way means that you are not setting a precedent for handing over cash, you know the bill will be paid and you can sleep easy knowing that you have alleviated at least the current crisis.
In my role I am in a position to make conditions when I'm administering money and I would strongly suggest to the client that she engages with CAP (Christians Against Poverty) or Stepchange in order to ensure that her financial difficulties are addressed.
Morecambe and Wise - the lost tape
Recommendations please for thorn- and nettle-proof gauntlets – if possible vegan


and this lady is lucky to know you .