Beth as a person certainly exists, but what she represents, and how much interaction she has with Nina is open to interpretation. I believe to Nina, she represents the 'career' her mother gave up for her. When all the younger dancers are being critical of Beth and saying she should move on, Nina defends Beth, saying that Margaret Fontaine danced into her 50's -- I feel she is echoing the message she would have heard from her mother, who delusionally believes if it weren't for Nina, she would have had a long and successful career.
I believe Beth is the volatile character we see portrayed in the earlier scenes, but I don't think any of the scenes of Nina visiting Beth in the hospital are real. The guilt she feels about replacing Beth, effectively ending her career, is fed by the guilt trip her mother has placed on her for cutting short her perceived great career, and therefore the scene of Beth saying she is nothing and stabbing herself in the face is Nina imposing her image of her mother's emotions on to Beth.
From the snapshots we get of the mother we see that it's clear she blames Nina for the loss of her career, and while she is on the surface caring and overprotecting, I think underneath there is a lot of resentment and a desire to sabotage Nina's career. You see this when she buys the cake, as a dancer she knows full well that Nina would not want it, and then puts a guilt trip on Nina by going to throw it in the bin. Also if you look at all the pictures she has painted of Nina, non of them are very flattering, and they are certainly not loving portrayals of a daughter - more like someone obsessing over the thing that has thwarted them.