How common is a bowel ileus after hysterectomy?

My mother is 72 and last monday underwent a hysterectomy.

She recovered well but the day before she was due to come home from hospital she started suffering from vomiting/nausea and diarrhoea.

She has got progressively worse over the last few days and is now, still in hospital, currently on a drip. She is still vomiting and unable to do any more than take sips of water.

I don't know what to expect. I fear she won't recover, the staff just keep telling me she need to "rest" her bowel but she has been like this for 4 days now and nothing seems to be improving.

It is quite common. The bowel gets handled during abdominal surgery and that, coupled with the drugs given during surgery often cause the bowel to stop working for a while (called paralytic ileus).
I know four days seems like a long time...no-one wants to see their loved ones ill and in pain...but she should soon be back on the mend. The important thing is that they do not try and 'hurry' things. She needs to let the bowel rest then gradually reintroduce fluids, then food. Hopefully you should see an improvement over the next few days.

an "illeus" after any surgery is very common, the drugs used to keep a person anesthatized during surgery cause the bowel muscles to relax and it takes some time for them to "wake up" again, and in the elderly, it takes longer. Your mother needs to be encouraged to get out of bed and move around, physical activity will get that bowel working again better than anything else that can be done.

It's a not so uncommon (wish I could give you percentage, but that may vary from place to place) complication after any abdominal surgery. The nurse is right in saying it needs rest to the bowels. Given time your mom will be OK.
All the best for her speedy recovery!