In the U.S., the most common word I hear for women that age is "girl". Unfortunately, there's isn't an age-neutral word like "guy" that you can use for women. Note that "boy" always refers to a child, but "girl" does not. (Even older women sometimes refer to themselves are girls. For instance, if a group of women spend an evening together without any men around, they might call it a "girls' night out".) This is probably because of differing social pressures. Women are taught to value youth and beauty, while men are taught to value power and experience.
The common options are:
- Girl: Very common, especially among 18- to 25-year-olds themselves. Somewhat informal. Usually paired with "guy".
- Woman: More formal. Often used to refer to women in abstract instead of a specific woman. Usually paired with "man". Sometimes used to emphasize maturity.
- Lady: Common in plural form, as in "ladies' night". Can be formal or informal depending on the tone and circumstances. Usually paired with "gentleman". In the singular form, usually refers to an older woman. Sometimes used in the traditional sense of "a woman with class".
Some less common options are:
- Young lady: Don't use this unless you want to sound old or archaic. People under 70 mostly use this phrase when disciplining their children.
- Young woman: If you use it informally, this will also make you sound old, but less old than "young lady". Like "woman", it's often used to refer to women in abstract.
- Lass: If you use this in front of Americans, they will think you sound Scottish. (Or Irish. We're easily confused.)
- Gal: Informal. If you are not a native of the southern or southwestern United States, this will sound a bit silly.
- Miss: Very formal. Normally only used in second-person. ("Excuse me, Miss? You dropped your bag.")
- Chick: Very informal and a bit demeaning.
If you see any others, post them in a comment and I'll add them to the list.
So here's my advice. If you're speaking casually, use "girl". If you're speaking formally or technically, use "woman" (or "young woman" if her age is important). If you're ever in doubt, use "woman". Only use the other options for deliberate wordplay.
I don't think you're showing a gender bias. This is a real problem in English, and even native speakers have trouble with it.