I'm not the world's greatest expert, but here goes:
The important thing is to be as quick as possible and not let your mum get cold. Roll her over and place a towel under her. Remove her nightie and put another towel over her. Have ready a bowl of warm water and a flannel. Face, hands, armpits, groin, under breasts. Keep the bits you are not washing covered with the towel. Then roll her on to her side and wash her bottom. Concentrate on the bits that will get sore, don't worry too much about the rest. Make sure you dry her properly and use Sudocream or similar if there is any redness. Keep talking, tell her exactly what you are doing as you go along, try to sound confident and emphasise that she will be all clean and comfortable with a nice fresh nightie. If she can sit up and help you at all, so much the better.
Hope your mum gets over her infection soon.
I used their body wash and shampoo on my mum for a long time. They kept mum's skin and hair in lovely condition as well as clean.
One thing you have to remember is, it is the towel drying that does the actual cleaning.
You may well find body wipes easier , also no possibility of accidental spills causing bet or bed linen to be wet.
Whatever brand you buy do make sure you can warm them up as whey will strike cold on her skin
Speaking of cold, I found it is best to ensure the room is really warm when bathing someone
Sorry if you already know this
Watch out for any areas going pink or red. They could be the start of a pressure sore and need urgent attention