Question: Do people with bipolar disorder also develop psychotic symptoms?
Answer: Certainly psychosis can be a part of bipolar disorder. Psychotic symptoms are not always present.
Bipolar disorder is understood by some as a disease of rate. That is -- a person is sped up. Their judgment is gone. They're full of energy; they need less sleep than usual. But often this can extend to actual hallucinations and delusions as part of the sped-up state of bipolar disorder.
Likewise if someone is severely depressed, they may also have psychotic symptoms that accompany that state, sometimes relating to being unworthy or filthy or frightened and paranoid that others are trying to harm them in their depressed state. So certainly psychosis can be present or not. When it is, it makes the situation that much more worrisome.