What's the best way to know if my mum is bi-polar?

It is hard to tell : From your question, it is hard to tell. We all have mood swings from time to time. Manic depression i is far more than simple mood swings. Manic depression ii is a bit harder to recognize, since the mood swings are more frequent and less severe. To know for sure, call a therapist and get her an evaluation. They can help you understand her condition.

Bipolar: Bipolar I and bipolar II, In the first, manic phases are more severe, and in the second, depressive phases are more severe. There is also cyclothymia which is a low grade version of bipolar disorder in general, where mood swings are not as severe in either direction, manic or depressive. Have mum evaluated by a psychiatrist to be sure.