There would not be an independent, control variable, or dependent variable because it is not an experiment. There is no causal relationship between two variables in a correlation research study.
However, this could be a research question for a quasi-experimental design that would utilize correlations:
Do those diagnosed with borderline personality disorder have similar levels of anxiety to those diagnosed with bipolar disorder? You would be comparing the anxiety levels of people with bipolar disorder with borderline personality disorder.
If you still want to use a correlational design, you could examine whether there is a correlation between stress levels in both disorders: Do people with borderline personality/bipolar disorder have high levels of stress?
