The short answer to the question “Do I need a woman’s bike?” is maybe. Maybe you do, and maybe you don’t but possibly you could go either direction with the fit.
It lays out into many variables, upper body to lower body and your flexibility/strength. Every person has proportions that their body lays into. Someone that is 5’10 and someone else that is 5’10 could easily fit completely different bikes.
Same Height but Different Bikes
Person, “Joan” is 5’10 with 34″ inseam and very limited flexibility.
Person, “Terry” is 5’10 with 31″ inseam and very flexible.
Joan will really need the woman’s fit on her bicycle, with a shorter upper body compared to her lower body. If she was to get on a standard fit bike the length of the bike may be too long. To fit Joan well, a shorter length of bike, or tube tube, is needed. Most womens bikes have these.
What Else is There?
The rest of the pieces of the bike fit puzzle for women are saddle type, and handlebar width. These two things can be accommodated on non-womens bikes but will need to be swapped out or changed down the road. Making sure you are on the right size frame is the most important and also the most costly if you get it wrong.
Not every woman needs a bike designed for women. In fact some guys need a womens fit bike. I would love if we got away from calling the standard fitting bikes “unisex” and the shorter length bikes “womens.” It should be standard and shorter. Make sure you find a shop you trust, and test ride. Some adjustment in size can happen with the stem length but not enough to make a bad fitting bike into a perfect fitting bike.