Part of anorexia nervosa is actually pushing those you love away. People with this disorder find it easier to be left alone and completely shut themselves off of the outside would. This actually feeds the disorder.
Everyone should have space but not the extent that she is after. It's part of the disorder. You need to be there for her. Visit her even if you spend it in another room from her. Show her you aren't going away no matter what. You really should do some reading on anorexia nervosa as well to help you understand what you are up against. It's a nasty disorder and the likelihood of relapse is very high.