You can't make someone take medication. If she wants to deal with it without drugs - completely possible, as my BF is bipolar and not medicated - the best you can do is support and understand her. If you think you're having a tough time, imagine how she must feel! Help her to focus her energy when she needs it most. Learn to recognize a manic or depressive episode, and the best way to handle it. Depending on your mom, sometimes the best thing to do is to do nothing! But the absolute worst is to begrudge her for it.
What is important is to acknowledge that this isn't something that can be cured with something as simple as a round of antibiotics. It's a process of finding what works and what doesn't. Some people react well to meds, some don't. Some best respond to therapy. Sometimes they need a physical outlet, sometimes a mental one.
So, instead of getting mad at your mom, try helping her out. If she's depressed, keep positive. If she's energized, let her direct that energy to something productive. If she's out-of-proportion angry or sad, say "Mom, I love you, let's stop this for a moment." Everyone's reactions will dictate how she will, in turn, respond emotionally.
You can't force someone to take meds if they don't want to, unfortunately. All you can do is try to be understanding and helping other people understand the illness is not her; her actions because of it are not a reflection of who she is when she's in the midst of an episode. If she ever seems to become a danger to herself or others, you can have her hospitalized.
Hang in there. It's tough living with bipolar disorder. I can only imagine how hard it must be from the outside looking in.