Well, rant aside, I put this to my wife, who is an occupational therapist.

She says that hanging on to handles while standing upright to wash, especially a foot wash, is highly unsafe. A tub transfer bench, which extends over the side of the tub so you sit down and then swing your feet in, is the professionally recommended way to go. If a shower chair, which sits inside the tub, is provided, she recommends a tub-side grab bar such as in the link Alice noted or a wall grab bar for support while your mother steps into the tub. Simpler and cheaper and if there is room and your mother doesn't want to get into the tub, a small chair next to the sink, positioned so she is seated when she washes her feet in the foot bath, might work.   

Bathroom equipment is not a covered service under Medicare in the US, although it may be covered under some insurance plans - purchase and installation is the patient's/patient's family's responsibility.