At the risk of stating the obvious, women are a different shape to men - they therefore have different requirements to ensure their comfort on a bike.
You don't have to ride the "step through" or "woman's bike". These are throwbacks to when most women rode in skirts. If you prefer riding in shorts, or leggings, there's no reason you shouldn't ride the same kind of "diamond frame" as a man.
As a woman your main problem comes when trying to get your "reach" sorted out, i.e. how far you stretch out on your bike. For women of 5'5" or under, this problem will be especially pronounced.
One alternative is to have a bike built specially for you. This is expensive so you'll be pleased to know that there are many changes that can be made to an off the peg bike to ensure it fits you. A CoBR member will suggest you make these kinds of alteration.
As most women have narrower shoulders than men you may therefore need narrower handlebars. The bars should be roughly the same width as your shoulders. If you have MTB bars you will probably not need to purchase new, just ask your CoBR member to cut down the existing ones.
Fit a shorter stem (the part connecting the bars to the bike) to reduce the distance between your saddle and the handlebars. This will allow you to sit more upright.
As you also have smaller hands than men you also need to adjust your brake levers so your hands can easily grip them. If this doesn't work, you may need what are called "short-reach levers".
And finally - if your inside leg is between 29" and 33" you will need 170mm crank arms (the items to which your pedals are connected). If shorter than this, go for crank arms which are 165mm in length.