The reason this conversation goes wrong is almost always the opening line. “You can’t manage on your own any more” is a verdict, and people argue with verdicts.
Ask instead what a good day looks like, and what has got in the way of one lately. You will usually get an honest answer, because it is a question about preferences rather than decline. It also gives you something concrete to solve: getting to the Thursday club, cooking a proper dinner, having someone to talk to on a Tuesday.
Frame the first help around that, not around bathing and dressing. Practical help is much easier to accept once someone already likes the person who is turning up.
