Mom broke her hip, and I am trying to make her home more elder-friendly while she is in rehab. While I have found lots of hardware that is available, I have not yet been able to find specs, such as how high a support rail on a regular wall should be, and particularly in the bathtub. Mom is about 5'2".
ADA (Americans with Disabilities Act) spec is 33"-36" off the floor for horizontal grab bars. And given 5'-2", I'd lean to the lower end of that scale.
Suggest you get one inside and outside the bath at whatever end is used most.
ADA.GOV has a lot of good information. (And overkill, like 42" bars at toilets, but I digress.)
Getting in and out of a bathtub is a dangerous operation for the mobility impaired. I have studied the ADA recommendations and outfitted our hall bathroom tub enclosure with two grab bars which is what I think is the minimum.
Last year even with these two grab bars I managed to fall backwards out of the tub. I didn't have a rubber mat in the tub and I turned sideways (facing the long wall), and took my hand off the long horizontal grab bar on the back wall. My soaped up feet slipped out from under me and I fell out of the tub onto my back. My fall was broken by the shower curtain and no injury.
I now have a rubber mat of a special type designed for "refinished" tubs which can be very slick. It keeps one from slipping, but does not adhere tightly with suction cups to the tub. That type is a pain to remove. My brother sent me this nifty type; I didn't know something like it existed. I'll bet the exact brand or similiar can be bought at a local store or online.
[EDIT This mat is about 29" x 16", is opaque, off-white and appears to be rubber rather than "vinyl". It has no plasticizer odor or any odor. It has dimples but not full suction cups like older ones.
It is very easy to pull up and I drape it over the horizontal grab bar after showering. I don't have the brand name, but I remember on the packaging there was the claim that it would work on "refinished" tubs (which ours is not). I think this must be a reference to epoxy refinished metal tubs. Our tub is an Americast steel tub which I purchased from a big box store about 25 years ago.]
In our hall tub/shower I installed a 36" bar horizontally on the long wall and an 18" bar vertically on the outside edge of the control wall. I haven't done it yet but I think it would be best to also install an 18" bar horizontally on the control wall. (In a tub/shower the controls are low and require the user to bend over to adjust them. A professional physical therapist I know told me that a horizontal bar just above the controls is important to the more infirm elderly.)
(I installed a curved shower rod which, despite being only about 6 inches out of straight, gives an amazing improvement in shoulder room in a tub/shower.)
If the tub is being used only for showering, the long bar is to be placed 33 to 36 inches above the floor of the tub. For sit down tub baths an additional bar parallel is to be installed much lower for getting up from sitting in the tub.
In a tub/shower I think one usually enters at the end by the control wall, whereas in a shower the entry is on the back wall (opposite the control wall). In this shower I was asked to put a horizontal bar on the entry wall and forgo the vertical bar. The towel rack is actually a grab bar and serves as support when exiting the shower.