I generally do not capitalize bipolar disorder, unless it's in a title of a thread or blog post.

As for the acronym used for bipolar disorder, there are a few out there. Many places like "Bp Magazine" use just BP. The acronyms BP1, BP2, BP-NOS are also common. I tend to use the "BP" acronym, for these reasons. Then, officially, there is BAD, meaning "bipolar affective disorder", but I'm not so fond of my illness having "BAD" as an acronym. Just my feelings. I have also, indeed, seen "BD" for bipolar disorder. "BD" makes sense, but I really think it is less commonly used than "BP", from my observations. When people write "BPD" it does indeed cause a lot of confusion. "BPD" only stands for borderline personality disorder. I think on bipolar disorder forums, members are used to people making that mistake, but do sometimes need clarification. I also think that many people with borderline personality disorder occasionally visit bipolar disorder forums.

The whole "I am [insert disorder/illness]" is an often discussed topic. One can't tell another person what they should or shouldn't say, but I am a member of the camp that does not equate myself with a disorder/illness. I always use "I have bipolar disorder". I, personally, feel that there is a heck of a lot about me that has ZERO to do with a mental illness.