First of all, I doubt you have a genuine bipolar disorder, it's probably the circumstances of your life that are creating bipolar behaviour, there's a big difference between bipolar behaviour and bipolar disorder. Bad things and good things happen in your life and it all depends on which one your focusing on at a particular time. Even IF you do have bipolar disorder, don't use it as an excuse to bail out of certain responsibilities.
You, on your own, can't substitute the male role model your kids need. It's a very tough situation your in, very tough, but for the sake of your kids you need to do everything you possibly can to find a positive male role model in their life, if you don't find one tomorrow, keep looking, if you don't find one this year, keep looking, don't give up. There ARE some good men out there, I know they're tough to find but they are out there. You must do everything in your power to find one and don't give up no matter what happens. I know you know all this, I'm just trying to tell you to keep working on it and don't give up, he's not going to fall threw the ceiling and onto your couch. Don't pick a man for you, pick the man for your kids (even if he's 800lbs with a bad comb-over and no job). You can't afford to be picky.
In the meantime, the kids need to have a happy and confident mom. Don't let your emotions from previous experiences run the show (thankfully you already know that, but keep reminding yourself). If your up and down and all over the place the kids will pick up on this and mimic you as that's all they know. Hold your head up high and the kids will thrive from your confidence (even if you have to fake it).