A bathroom lock gives her privacy, and it also gives a fall a way to stop anyone from getting in. The useful comparison is not the finish or the price. It is how someone in the hall can open the door when she cannot answer.
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Look for an outside release
Most privacy sets have a small hole in the outside knob or rose. A thin tool pressed into that hole releases the lock. Check the product listing or the printed instructions for the release method, then confirm it on the actual lock before you buy. A set with no outside release, or one that needs a special key you will not keep nearby, is a poor match for a bathroom door on her night route.
Compare the inside control
Check how she locks it from inside. A push button or a simple turn is easier than a small thumb latch that needs fine grip. If she uses a walker or a rollator, stand where she stands and try the control with one hand. The control should lock and unlock with a clear, low-force motion.
Check fit before you check the look
Measure the door thickness, the bore hole, and the backset, then compare them to the lock's specification sheet. A set that does not match the door will not seat properly, and a loose lock is harder to release from the outside. Ask the seller whether the outside release works on your door thickness.
Test it before anyone relies on it
Install the lock, close the door, lock it from inside, then go to the hall and release it with the outside tool. Do this in daylight and again with the night lights on. Time how long it takes to open the door from the hall. If the release is hard to find or the tool slips, the lock is not ready. Keep the release tool in the drawer nearest the hall, and tell whoever might come to the house where it is kept.
Write it down
Record the lock type, whether the set is privacy or passage, the location of the outside release, the tool needed, the door thickness, and the test date in your own notes. Keep that page with the tool, so the next helper finds both in the same place.