My sister is bipolar it was never diagnosed when she was a kid but later as a young adult.She was a very difficult person to deal with because one day she was very easy going and the next she was mean as all hell.Even after she got diagnosed and received therapy she had some difficultly she was married for a few years and got divorced but that rift was a two way fault for sure.
Now though she is much better she can fairly well manage her disorder and she got married again to a much better more understanding and none self centered husband.
I agree with Skybird though you can not "cure" being bipolar but a person suffering from it can if they chose to do so manage it and be a decent person to be around most of the time(hell no one is perfect right?).
That seems odd what your girlfriend said:
"she does not want injections and has an aversion to popping pills but may be willing to take a pill if it doesnt require a prescription."
That seems like wanting to avoid something to me she must know that any medication to help her would be prescribed.
Seems like she wants to avoid being labeled as something but to get any help she has no choice even if nothing is prescribed they are going to you are this or that.
Your friend needs to see a professional though she may be bipolar she may be something else.