She states that she'll drive herself to the grocery store or make her own beauty appointment and go on her own, although she does not have a car and has not driven for several years. Attempts to invite her with statements such as, "I'd enjoy your company" are met quickly with no responses. This client lost her husband/caregiver a few weeks ago.
If it is your job to get her out of the house, then I might look into why she may not want to go.
Maybe, she's still grieving the death of her husband and needs more time.
Maybe, she suffers from incontinence and is afraid she'll wet or soil herself if she goes out. Does she wear diapers? Some people are uncomfortable with that. They are afraid of having an accident.
Maybe she feels dizzy or weak and is afraid of falling. Does she use a walker?
Maybe, she's depressed and needs to discuss it with her doctor.
Maybe, it's none of those and she just doesn't know how to get ready to go out. Maybe her husband did that for her. Sometimes, you just get them ready and escort them out the door, assuming you have authority to do that.
She just lost not only the person she shared her life with, but the one person she could absolutely rely upon to love her in spite of all her impairment, and the person who saw that her needs were met. And this was only a few weeks ago. My gosh, give this poor lady time!
Continue to offer to take her out, but do it gently and without any implication that she "should" be ready to go out. For now it might be better to spend time with her in her own familiar environment. Look at scrapbooks. Play cards. Be her social lifeline. Make a grocery list with her and pick up her essentials.
In previous generations, for a new widow to be out and about within weeks of the death would have been scandalous. I am glad we are past that outlook, but I'm afraid we've thrown the baby out with the bathwater. People grieve in their own ways and at their own pace. Who says the person "should" be ready to go to the beauty shop now?
The ability to interact deteriorates with hearing loss, the person feels uncomfortable and gradually prefers just to stay home.
Add in bladder or bowel issues, and the confidence loss accelerates and comfort level decreases.
I don't think people should be pressed to go out and socialize just for the sake of it. I think they're more comfortable if people they do know visit them, in the comfort, security, and awareness of their own surroundings. Then they can feel safer, less challenged to be in an unfamiliar environment.
One of the hardest parts of caring for older parents or family members is putting ourselves in their places, when they themselves often don't understand the dynamics of the situations.
Putting pressure on someone who doesn't want to be social will only make them more uncomfortable, and you more unwelcome, especially if you're a paid companion and not a relative or someone this woman has known for years.
I'd say back off and give her the space she needs.