The dying back of the stem you removed may have been caused by under watering or not enough light, not necessarily overwatering and root rot. White Birds are pretty hard to overwater if they are in good sunlight and they are not left sitting in water.
Root rot is really root suffocation caused when the soil is kept waterlogged and oxygen cannot penetrate to the roots. It is not a disease that spreads and does not warrant replacing the soil. It simply requires allowing the soil to dry out more. Not sure if this also contradicts your mother, but that is how it works.
Putting drainage material in the bottom of pots is an outdated and discredited practice and is not recommended. Proper drainage occurs when the pot is not too large, the potting mix is porous throughout and the pot has drain holes.
I think the best things you can do for your White Bird now is to improve the light and remove all the soil from the top surface until you start to expose some roots. After removing that excess soil, allow the top half-inch of remaining soil to dry before adding just enough water for the top half-inch to dry again in about a week. You will have to experiment a bit to determine the right amount of water.
The available light between the windows is much less than you realize. It is barely adequate, but your plant would do better if placed in front of one of the windows. This is a plant that prefers direct sunlight.
