What to do when your parent can no longer get up to use the bathroom?

I would say try diapers. As others have said, catheters are an option, but are uncomfortable for some people. Diapers can be somewhat embarrassing as from what you said you or someone else would have to change her, but they may be the best option since you have a bad back. Using a bed pan could be helpful, but also can be embarrassing. A bedpan does feel more like a toilet than a diaper, though, so it is more comfortable for some people. Just be sure to use a towel on the edges because it can be cold and one under it in case of leaks.

Get professional help in, at least for the short term, and learn how to support your mother with transfers.

A hospital bed would be easier for her to get out of and into.
There are bedsticks, turntables, stand-aids and all sorts of other machines and devices to assist mobility.
As for supporting her - if this takes any physical strength or puts strain on any part of you, you're doing it wrong.

Do you have any outside help at all with her care at the moment?

I would touch base with your Mom's physician... he should be able to order a PT/OT evaluation and therapy. If therapy does not help or is not warranted, you can use protective undergarments and home health aids to assist as may be afordable, on a daily basis (though most HH agencies in my area of FL require a minimum of 2 - 4 hrs. per day). Another possible option is a live-in caregiver to assist. Another option may be to get training on using a gait belt to help your mother to steady and walk as well as stand and sit safely. But this will not allow a full lift if she cannot assist at all. Hoyer lifts are often used when people cannot assist at all, but be aware that by the time you connect the device and maneuver your mother to the toilet, she may not be able to "hold it" until she is seated on the commode. It is very difficult to lift someone without assistance if they cannot help such as pulling themselves up or balancing to steady themselves. Time to reach out to some other resources for assistance. (If she qualifies for palliative or hospice care, aids will come daily to help... paid by Medicare. Her physician can request such an assessment from local hospice).

Foley catheters are an option, but my mother HATED it, was uncomfortable, embarrassed, and having worked for years in SNF's, these can increase chances of UTI's and other complications. If you mother has dementia, she may be annoyed by the Foley and try to pull it out, causing injury. I would say this is a very last resort.

I would touch base with your Mom's physician... he should be able to order a PT/OT evaluation and therapy. If therapy does not help or is not warranted, you can use protective undergarments and home health aids to assist as may be afordable, on a daily basis (though most HH agencies in my area of FL require a minimum of 2 - 4 hrs. per day). Another possible option is a live-in caregiver to assist. Last option may be to get training on using a gait belt to help your mother to steady and walk as well as stand and sit safely. But this will not allow a full lift if she cannot assist at all. Hoyer lifts are often used when people cannot assist at all, but be aware that by the time you connect the device and maneuver your mother to the toilet, she may not be able to "hold it" until she is seated on the commode. It is very difficult to lift someone without assistance if they cannot help such as pulling themselves up or balancing to steady themselves. Time to reach out to some other resources for assistance. (If she qualifies for palliative or hospice care, aids will come daily to help... paid by Medicare).

For starters, make sure she is wearing some kind of diapers. And make sure you have her lift chair lined with waterproof pads, as to not ruin the chair with pee or poop. You can also hire an aide(s) to come assist her on and off the bedside commode as well. They will use a gait belt to help them pick her up. You can also get a Hoyer lift, but if her bedroom is carpeted, I was told by my husband's hospice nurses that a Hoyer lift will ruin your carpet, so just be aware of that. And of course, you can always have a catheter(either permanent or not)put in as well. Best wishes.

Hoyer lift for now, but ultimately adult diapers. My dad used to say “we all come into this world using diapers and we all leave in them” I hope you won’t risk injury to yourself, take care of your health

My first recommendation is to get her some PT to buy you a little time because once someone can no longer stand and pivot caregiving becomes exponentially harder. Since you are not able to help her even minimally your best bet for the long term is going to be a patient lift (hoyer is one brand), although a sit-to-stand lift may help if she can keep herself upright once she is on her feet.