I have IBS and know of several others with it too and I would say that most people with it understand which foods give them the bloating, cramping, pain, diarrhoea, constipation, etc. So ask your DD to write a list of the foods that she thinks are her triggers. Common ones for sufferers of IBS are wheat/gluten, nightshades (peppers, potatoes, aubergines, etc), spicy foods, fatty foods, alcohol, and in some cases dairy. However, I can eat dairy with no problems at all. And that's the thing - everyone has their own list of triggers.
When I was diagnosed with probably IBS the doctor recommended I cut out wheat/gluten for one month and see if that helped. If it didn't make any difference he suggested I add it back into my diet again and try doing the same with dairy. He advised me to avoid fried food, Indian/Chinese food, and nightshades, since those things make me feel so ill. It IS restrictive and it can be difficult and annoying when I'm out with friends, at someone's house or limited by what food is available - such as while travelling - but not eating the things that make me feel ill has made a huge, positive change in my life.
Your DD's MH issues and self-restricting behaviours with food should be addressed with therapy, as she needs to eat properly for her health and with IBS, quite frankly, her diet is going to be limited enough without her being faddy about the things she CAN eat!