How do I get the apartment manager to install a shower grab bar?

When you asked the apartment manager about installing the safety bar, how specific were you about what the PT had recommended? Did you say "please will you install WonderGrab 775 bars, fixed to the wall with NeverFail bolts" or did you just tell her that the PT had recommended a grab bar?

The advantage of the clip-on device is, of course, that it doesn't compromise the integrity of the wall structure or décor. Sadly, however, it probably does compromise safety. Check out the *exact* specifications of both products on the manufacturers' websites, print them off, take them to your manager, draw her attention to their respective safety performances, and remind her that we wouldn't want anyone coming to harm because of failures in safety fittings now, would we.

Also: what are the walls made of? If they're tiles on plasterboard over battens, you probably can't fix a secure grab rail to them anyway.

I would imagine the apartment management would not want to invest in paying to have that grab bar installed. Would showering using a shower seat be an option? I know my mother preferred baths over showers but in the end she received showers due to the difficulty getting in and out of the bathtub.
Review the language in your lease to assess what your landlord is required to provide in episodes such as this. I would do this first.
See if you can apply the ADA ( Americans with Disabilities Act) in this situation as a motivator for the rental office.
I am not sure if you are allowed to make modifications in the apartment for someone not on the lease. They can say the apt was rented “to”you and “for” you thus deny to allow nor pay for bar installation.
In the interim see if she’ll use the shower first. That will solve your immediate problem as you work through the details.
Good luck!

If your apartment has a tub and not a dedicated shower there are grab bars that clamp securely to the side of the tub that are perfectly safe - I don't trust anything that just uses suction thought. There are also products that stretch between the ceiling and floor (superpole is the one we had) which do not require drilling holes, but they are pricier. A good sturdy shower chair is a must, a transfer bench might be helpful if the problem is stepping over into the tub/shower. And since this is to be a temporary arrangement you might ask about renting this equipment rather than buying things that may not be needed in a few months.

Use the clip on device. Mine works fine.

There are bars that fit over the tub side to help get in the tub. I have used the suction type. I had a man pull on it and it never came off. Just check it each time before using it.

Not sure if the disabilities act refers to certain aged apartments. Those built before the law. Ones built for 55 and up usually have disable accessibility. With Mom being temporary.