According to www.dualdiagnosis.org, 56% of people with bipolar disorder suffer(ed) from addiction to drugs or alcohol at some point. According to www.drugabuse.gov, the rate for general population (in America) is 8.9 percent.
Obviously there is something about bipolar disorder that correlates with high addiction rate. While I am not a medical professional or addiction counsellor, I will hazard a guess that bipolar makes you predisposed to addiction, not the other way round. There are some drugs that can trigger a bipolar episode (in particular marijuana and LSD), but they do not create bipolar disorder in a mentally healthy person. They may only make it manifest earlier.
There are a few obvious reasons why bipolars tend to become addicts. One of them is self-medication. I used to self-medicate my depression with alcohol for years – it seemed to be the only way to make the black dog go away for a few hours. I knew that alcohol is a depressant and on some subconscious level I probably realised that I am making things worse for myself long term, but at those times the only thing that counted was quick relief which the bottle provided. The same scenario happened daily: I’d be terribly depressed, I’d get drunk, depression would be replaced by euphoria, I would do some really stupid things, go to sleep, get up in the morning and scream “F–K!!!” (I never blacked out; I always remembered what I did the day before, and it was always terrible and make me more depressed.) Repeat. Repeat.