A phone in the living room does not help at 3am on the bathroom route. The install is simple, but the order matters. Pick the spot by where she reaches, not by where the outlet happens to be, then program and test the phone from the places she will actually be when she needs it.
Local option: New Plan Care gives families in the St. Louis area in-home help so a parent can stay home: companionship, help with bathing and dressing, meals, and overnight care. Call (314) 405-0887.
The install order
First, sit her on the bed edge and mark where her hand lands on the nightstand without leaning. Choose that spot, and let the outlet adjust to it, not the other way around.
Second, run the cord so nothing crosses the bed-to-bathroom path. If the cord has to cross the route, the spot is wrong, so move the phone or change the outlet plan before you go further.
Third, charge the handset fully before the first test. Check that the base sits steady on the nightstand and that the handset seats in its cradle without rocking.
Fourth, program the one number you want reached at night, and label the handset with that number and one short instruction in large print.
Test the fall, not only the ring
A phone that works from the bed is not the same test as a phone that works after a fall. Lie down on the floor beside the bed, where she would land, and see whether you can reach the handset from there. Test the call from the bed edge and from the floor, and ask the person who answers whether they can hear clearly and whether they can tell where the call came from.
If the base is out of reach from the floor, move it. A cordless handset she can keep in a pocket or on a belt may reach where a base cannot.
Who answers and what to write down
Name who answers at night and the words they should use to find out what is wrong. Write down the spot, the cord route, the bed-edge call, the floor call, and whether the speaker is clear from the bathroom door. Keep that page with the night log. If nobody is available to answer at night, settle that before the install, because the phone cannot make that decision for your family.