Anxiety is very common in people with bipolar moods. In fact, anxiety is typically the first sign of mental health problems (often it is present in childhood) for people who later develop bipolar.
As a psychiatrist, I am aware that we have fewer useful long term treatments for anxiety in bipolar than we do for the mood swings of the disorder.
Some of the things that people use to help anxiety can actually make bipolar worse (marijuana, gabapentin, and sometimes antidepressants). The most common treatment for anxiety (benzodiazepine medications like Valium, Xanax or Ativan) is much better for treating short-term anxiety. But the anxiety associated with bipolar is usually long term.
A recent study from the Systematic Treatment Enhancement Program for Bipolar Disorder suggests that psychotherapy is often the best answer.
The study (Do Comorbid Anxiety Disorders Moderate the Effects of Psychotherapy for Bipolar Disorder? Results From STEP-BD) looked at 269 patients who either had an anxiety disorder (as well as bipolar) or did not. The patients were then randomly assigned to medications plus “collaborative care” (medication management and general counselling) or medications plus psychotherapy.
The study found that the addition of therapy to medication management made a significant difference for those patients with an additional anxiety disorder, but did not make a significant difference for those people with bipolar who did not have anxiety.
The picture at right shows that there was no significant difference in the percentage of people with bipolar who had full recovery (had resolution of almost all of their symptoms) who did or did not receive psychotherapy, 
except for the group with an additional anxiety disorder. In that group, the percentage who had full recovery was much lower (compared with those without anxiety) if they only received medication management.
However the addition of cognitive behavioral therapy (CBT) for their anxiety reversed that difference. In fact, with therapy, patients with anxiety actually did slightly better than those without anxiety.
There were benefits from therapy for all people with anxiety disorders, but the findings were particularly marked for people with generalized anxiety or posttraumatic stress disorder. These are the results cited in the article (collaborative care meant medication management):
Sixty percent (N=18) of participants with current generalized anxiety disorder recovered with psychotherapy, whereas 19% (N=4) recovered in collaborative care… Sixty-four percent (N=9) of participants with current PTSD recovered with psychotherapy, whereas 40% (N=4) recovered in collaborative care.”