I may not be the best person to answer this, being a man, but I've lived in Bangalore for 6 years, and in my 3rd person perspective on this, Bangalore (and southern India in general) is much safer than the infamous parts of the country, and doesn't feature as often in reports of sexual assault.
In recent years, there have been a few violent street robberies, though mostly of men, in some parts of the city.
The best precaution is to avoid being alone in deserted and unfamiliar areas.
I recommend reading a few news reports of crime in the city to get an idea. Bangalore Mirror could be a good resource. Such incidents are relatively infrequent though.
Overall, crime is hardly a concern while living in the city. People love the food and pubs, and hate the traffic.
All the best, and welcome to Bangalore!