Mumbling... not sure how to handle this?

Speaking as a mumbler the frustration you feel wanes in comparison to ours . We are highly tuned to pickup any feelings of disgust or impatience or frustration or repulsion of us .In turn we react accordingly.
on the other hand when treated with love ,dignity,respect and patience we respond by trying harder the monumental task of speaking

She's making a game of this to see your reaction.

I go through that with my wife. She has aphasia and dementia and frequently does the same thing. Can't speak clearly. Some times she will stutter. Other times she will just look at me like I am completely stupid.
I do know that she can read aloud pretty good. She can read the tv commercials.
Flash cards or pictures and such as recommended just might help.
A speech therapist might be able to help set up some cards or pictures.

I would suggest placing a large "white board" next to her bedside and see if she can write, e.g. "water", "food." Keep it simple. One word.

Would it be possible for your client to write what she wants?  I had an aunt in a nursing home who refused to wear her hearing aids and we her family were tired of yelling to communicate with her.  I thought of bringing her a dry-erase board so we could ask her questions.  Maybe this would work in reverse for your client?

Try mirroring back what you think she said. Small bits at a time. Hopefully she can at least agree or disagree with your interpretation.

If she can turn pages, I would create a binder with pictures of various snarios and help her understand each one. Use clear plastic insert pages to insert the photos and each can be wiped if necessary.

Maybe paralanguage: Hmm. Uh-huh. Sigh.

Maybe affirmative comments: I hear you. Good point. Gotta think on that one.

When you can, post something on your profile about ur patient. It helps us to help u.

There 's more here than dementia if she is bed bound. Did she have a stroke? If so, she may not be able to talk. Who is paying you for her care? Family? Is there someone you can question about her health history. Maybe some speech therapy will help her.

Put in search "Talking Boards for Stroke Victims" Here is what I found.

https://www.hopkinsmedicalproducts.com/images/xxl/Picture-Communication-Board.jpg

This way she can point to what she needs. There r some sophisticated ones but they are pricy. Maybe you can put one together cutting out pictures from a magazine. It has to be as frustrating for her as it is for you.

Sometimes, I think we can try to anticipate what may be the matter, while keeping in mind that with dementia, the patient's mind may be making them make sounds that are not really understandable. She may not even realize what she is saying herself. So, I'd try not to stress over this. You might check to see if she's wet or needs changing. If it's been awhile since her meal, offer a snack or beverage. Adjust her position in bed or rearrange her pillows to make her more comfortable. If her skin is cool, put on another blanket, if hot, adjust accordingly. Maybe, she's bored, turn on some music or read to her. Just try to cover all the potential things. You might even say outloud, I'm not sure what you want, but, I'll do my best to help you. So, if she does understand, that will give her comfort.

You might discuss it with her doctor too, to rule out any pain that she could have that she is not able to communicate about.

You might also check out online videos by Teepa Snow on dementia. She has a method of how you can hold the patients hand and touch their arm in order to get an idea of how they are feeling and if they are in pain, if their communication is not good. I'm not that familiar with it, but, recall seeing it on You Tube. She has a lot of suggestions for helping understand and manage care.

Even those who speak clearly sometimes can't find the right words, can't articulate what it is they want or just don't make sense. With my mom it was that she would call but not know what was wrong when I got there so I went through my list of things she might need - are you in pain... and where? hungry? thirsty? need repositioning? need changing? want the radio on? want to get up? etc etc
Sometimes we just couldn't figure it out so I did what I could to comfort her and sometimes it was part of her pattern of anxiety and dementia to call repeatedly for no reason.

Does she have an illness that would cause this mumbling? Something with her speech or vocal chords?

Does she have dementia?

I suppose the reason doesn't matter since if her mumbling is the symptom of something medical it's probably not something you can fix.

I wonder how long you've been working with her. Maybe you can get used to her mumbling and begin to understand her.

You're only other recourse is to ask her to repeat herself which I know can be tedious for you and annoying for her but you have to know what she needs. If sh's lucid explain to her that you're having difficulty understanding her and ask her if she can speak more clearly. You have to be able to understand her so she can communicate her needs to you.