Diagnosis of bipolar from Wikipedia:

"Diagnosis

Diagnosis is based on the self-reported experiences of an individual as well as abnormalities in behavior reported by family members, friends or co-workers, followed by secondary signs observed by a psychiatrist, nurse, social worker, clinical psychologist or other clinician in a clinical assessment. There are lists of criteria for someone to be so diagnosed. These depend on both the presence and duration of certain signs and symptoms. Assessment is usually done on an outpatient basis; admission to an inpatient facility is considered if there is a risk to oneself or others. The most widely used criteria for diagnosing bipolar disorder are from the American Psychiatric Association's Diagnostic and Statistical Manual of Mental Disorders, the current version being DSM-IV-TR, and the World Health Organization's International Statistical Classification of Diseases and Related Health Problems, currently the ICD-10. The latter criteria are typically used in Europe and other regions while the DSM criteria are used in the USA and other regions, as well as prevailing in research studies. The DSM-V, to be published in 2013, will likely include further and more accurate sub-typing.[47]
An initial assessment may include a physical exam by a physician. Although there are no biological tests which confirm bipolar disorder, tests may be carried out to exclude medical illnesses such as hypo- or hyperthyroidism, metabolic disturbance, a systemic infection or chronic disease, and syphilis or HIV infection. An EEG may be used to exclude epilepsy, and a CT scan of the head to exclude brain lesions. Investigations are not generally repeated for relapse unless there is a specific medical indication.
Several rating scales for the screening and evaluation of bipolar disorder exist, such as the Bipolar spectrum diagnostic scale.[48] The use of evaluation scales can not substitute a full clinical interview but they serve to systematize the recollection of symptoms.[48] On the other hand instruments for the screening of bipolar disorder have low sensitivity[clarification needed] and limited diagnostic validity.[48]"

The part in bold is about differential diagnosis: what needs to be EXCLUDED.

Where do you see (in the above) that psychiatrists cannot diagnose a patient who is on alcohol and drugs?

The process of excluding other hypotheses is called Differential Diagnosis. When symptoms A, B, and C are present, there might be different causes of symptoms A, B, and C. Doctors form hypotheses about the causes and try to exclude them via a process of elimination (similar to what you would do on a standardized test).

alcohol and drug use is one of the many hypotheses that are alternatives to the hypothesis of bipolar, but just one of many, and to say that a patient needs to have zero level of use to be diagnosed is extreme.

So many bipolar people also use drugs and alcohol that if doctors start to refuse diagnosis and treatment until and unless the patients stop all use, the situation will become disastrous.