At what height should support handrails be mounted in a home?
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.)