A little further information for you:
Alcohol interferes with bipolar meds. It is a depressant.
There are a whole lot of levels of bipolar disorder, from often suicidal and often hospitalized, nearly schizophrenic, to high functioning.
A good analogy for bipolar disorder: If you are standing on a high dive as a non bipolar, your body starts producing chemicals in preparation for the dive.
A bipolar on the high dive would produce the chemicals of one preparing to dive from a cliff.
The height of the cliff - and the depth of the water - depends on the level of bipolar disorder.
In severe cases, you could say it's a very steep and high cliff they are standing on, and a shallow stream they are jumping into.
Here are some famous bipolars, some with drug and/or alcohol problems, and others without. It does give some bipolars the desire to "self medicate."
IMHO yes, someone with bipolar would have a harder time giving up an addiction because of the "multi disease" aspect...
...but - that's not your problem 
:
Sir Richard Branson
Patty Duke - (suspected previous drug abuse, was given drugs as early as age 13)
Carrie Fisher (who is a recovering addict; see the movie POSTCARDS from the EDGE, based on her life in movies and with her mother, Debbie Reynolds, an alcoholic)
Adam Ant
Dick Cavett
Mel Gibson, alcoholic (unknown if recovering)
Jane Pauley
Brian Wilson, recovering addict
Amy Winehouse, addict-alcoholic, deceased
Catherine Zeta-Jones
Richard Dreyfuss
Britney Spears...