When she talks to these companies, they do not assure her that she would get help if she falls or needs medical help when she is away from her apartment.. Maybe if she could try one without having to stay with them, she would get the coverage she needs? None of them allow tryout periods as far as we can tell.
If it's limited to medical protection, I assume there would be an obligation to call for medical help, but whether or not there would be an obligation for a bus driver or street car operator to provide medical assistance him or herself, I don't know.
There may also be made an argument that if she's prone to falling, she shouldn't be taking that kind of public transportation.
On that issue, you might want to explore the small bus services, which typically are more flexible and can provide door to door service for a nominal fee. In my experience, they're wheelchair equipped with platforms that can be elevated and lowered for wheelchair accommodation.
In a large city, such as Detroit, incidents will occur. There have been situations in which people have been assaulted on Detroit buses. Would the drivers have an obligation to protect the passengers? Legally, I don't know if they're obligated to get physically involved, but I am sure they are required to report the incident to the police for assistance.
As to a fitness center, that's a slightly different story, if your elder signed an indemnification and hold harmless agreement, which in my experience most workout centers require. Typically it would require that users hold the facility and its employees (along with agents, etc.) harmless if your elder is injured while on their premises, whether from someone else working out there and accidentally hurting her or whether from defective or improperly maintained equipment.
There was a case more than a few years back in which a Michigan woman sued a fitness center after being injured on allegedly improperly maintained equipment. The court ( and I don't recall whether it was an appellate or the Michigan Supreme Court) held that since she signed the indemnification agreement, she could not recover from the fitness center.
Do what "really protect her"? What companies is she [your Mom?] talking to? Do you mean a gym membership?