I know that road bike manufacturers do make smaller bikes for shorter people and for women. I don't think they are more expensive than other road bikes, but road bikes in general do cost more. I'm not sure about other types of bike.
Here is one link by Giant which will give you an idea. http://www.giantforwomen.com/bikes
. It has more types. If you google "fit on women's bikes" or something like that, you can get more general info.
Even if you just read about what a good fit looks/feels like, you might be able to get an idea when you go to try out. The other thing you have to watch is that sometimes what's billed as a women's bike is just a different coloured version of the men's. When I bought my roadbike, I bought a small, which was different from the men's, but they went as low as xxxsmall, depending on the brand.
You should be able to stand over the bike comfortably (when there is a bar) and put one foot down with just a bit of a tilt when stopped.
This is a really good women's forum where you should be able to find questions about bikes for short women.