It could. The agency likely will investigate the severity of the disorder, treatment efficacy (past and current), treatment compliance, prognosis, and other variables such as past episodes of severe depression or mania. The issue (hopefully) would be whether you might pose a risk to the child, such as through abuse, neglect, confusion, or impaired judgment, during a mood episode.
A diagnosis of bi polar disorder in and of itself will not prevent a person from qualifying to adopt. A social worker will interview the applicant and gather information from the applicant's psychiatrist to determine how well managed the condition is and if/ how it would impact the applicant's ability to parent a child in a healthy manner.
It depends on the type of adoption. Mental illness will most likely not preclude a step-parent or relative adoption where a home study is not required. Consideration of the illness and how it is managed will be subject to greater scrutiny in a private adoption or adoption from foster care. It is not an automatic rule-out though.
Before being approved for adoption, potential parents are closely reviewed. This includes their medical history for both physical and psychiatric illnesses. Having a mental illness is not automatically disqualifying in and of itself, but you will have to show that you can care for a child, and a qualified doctor will have to agree.