I would go and see a psychiatrist. Bipolar disorder primarily has temper issues in the manic phase of the illness. It would be accompanied by things like pressured speech, lack of sleep, increase in goal directed activities, reckless behaviour, etc.
If you always lose your temper - chances are it isn't a bipolar symptom. Doesn't mean something else isn't going on.
Anger management classes can really help out. My father went to them with a lot of success.
Yes this can happen as part of bipolar. It has happened to me at times. There can be a low frustration tolerance and sudden emotional reactions. However it would depend on what else was occurring as to what might be happening as there are other causes for this including everyday issues with anger management and there is much more that has to occur for bipolar to be diagnosed within a psychiatrist's professional discretion. If you have never seen a therapist it would be worth discussing this with one. If you are seeing a psychiatrist and are diagnosed with bipolar it would be worthwhile to discuss this with them further so they could see how to best help you.