Poor things, it's too bad that you had to run into such terrible luck. I see what you mean about spotting the beginnings of dropsy. Sadly many fish that reach this stage of infection don't make it. If you still want to go ahead and treat her given the prognosis, I recommend a broad spectrum antibiotic, like API's Triple Sulfa or a combination of Maracyn I and Maracyn II together.
It would be best to treat her in a different container with gentle aeration. Keeping the temperature on the low end of the betta's range (75-76F) is a good idea. It will help slow the progress of the bacteria. I always recommend that anyone using antibiotics read this article so that they have an understanding of how antibiotics work, the risks involved, and how to use them responsibly: http://edis.ifas.ufl.edu/fa084