With bipolar people, is it possible to decrease or stop the mood swings?

With Treatment. Yes, mood swings can be managed and sometimes eliminated through proper and consistent treatment. Treatment will usually consist of a combination of talk therapy and medication therapy.
Definitely. There are many medications, the so called "mood regulators" that do this.
Mood swings. If you have been correctly diagnosed with bipolar disorder, medications with mood stabilizing properties are the most effective. These can be traditional mood stabilizers, such as lithium, depakote, tegretol, trileptal, lamictal, topirimate, or gabapentin. Atypical antipsychotics are often used during the acute stages of mania and less often for maintenance therapy. Healthy sleep habits are a must.
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. Ideally, yes, mood swing intensity will decrease.