The fastest diagnosis of bipolar disorder can happen when a person has a sudden break into severe mania - bad enough to be hospitalized. Even then, other conditions will have to be ruled out first. Is the patient having a bad reaction to a prescription medications? Does he use illegal drugs? Is there a brain injury or tumor?
Other questions include whether the patient has a history of behavior that would indicate schizophrenia or a similar illness, or of clinical depression. They must be checked for Lyme disease and epilepsy, as well as other illnesses.
If the primary symptoms are hallucinations and delusions, the initial diagnosis might be Brief Psychotic Disorder. This illness appears suddenly with severe symptoms, but goes away in less than a month and can last as little as a single day. Time may have to pass to see if there's resolution or if other, non-psychotic bipolar symptoms appear, but treatment can begin right away.
Of course, this is a very simplified description of the initial evaluation of someone who shows up at an emergency room with serious symptoms that indicate a mental disorder. Each situation has to be evaluated according to the symptoms and patient history.
Fallon, B. A., et al (1995). Late-stage neuropsychiatric lyme borreliosis differential diagnosis and treatment. Psychosomatics, 36, 295-300.
Cleveland, M. (2001, August). Systemic Lupus Erythematosus. HealthAnswers, Inc.
Evans, D. L. (2000). Bipolar disorder: Diagnostic challenges and treatment considerations. Journal of Clinical Psychiatry, 61, 26-31.