To be diagnosed with bi-polar you daughter has to see a child psychiatrist. Her doctor or you insurance will reffer you to the right psychiatrist. I work with a child psychiatrist and it takes him 4-5 sessions to compleate the assessment. There not blood tests to test for bi-polar but the doctor will observe her and ask many questions. The diagnosis is based on observation and the answers to the questions both by you, your daughter, teachers and her Medical History.
psychiatric assessment, or psychological screening, is a process of gathering information about a person within a psychiatric or mental health service, with the purpose of making a diagnosis. The assessment is usually the first stage of a treatment process, but psychiatric assessments may also be used for various legal purposes. The assessment includes social and biographical information, direct observations, and data from specific psychological tests. The psychological tests that are used will be specific to her age. The psychiatrist will give you recommendations of what services your daughter will need such as medication, therapy usually both.
The problem is I am not sure that you can make an adult daughter see a psychiatrist if she does not want to go. You can suggest that but unless she is a danger to herself or others you can't take her to the hospital.