This is something I've been wondering about, the effect of T on mood with bipolar disorder. I have bipolar I, and I'm pre-T. I now have a trans friendly doctor and I'm doing my research before getting started (and waiting out a long probationary period at work).
I just saw my new doctor last week and we talked about this very thing. I was concerned about the potential for mood swings, even though my bipolar is well managed for a number of years now. I remember when I was on birth control many years ago, before my bipolar diagnosis, I had problems with mood when the hormone levels changed weekly. My new doctor is very trans friendly, and teaches other docs about administrating hormones and working with trans patients, so I trust his experience.
So, in my case, the doctor and I agreed that the daily gel or patch will be a better place for me to start and see how that goes, as opposed to injections every week or two, given my history. The gel/patch are far more expensive, but I should get coverage when my benefits kick in. Even if I had to pay out of pocket, it would be worth it not to have extra emotional upheaval. Hope this helps!
Also, it may worth it to keep a daily mood tracker or a journal to follow your mood vs injections/T application.