It seems like fast (with the exception of Tisha B'av and Yom Kippur) is a time bound Mitzva. I exclude Yom Kippur and Tisha B'av because they are all day fasts, so they don't seem to be just time bound Mitzvos.
What makes women obligated to fast on Tzom Gedalia, Asara B'Teves, Taanis Esther, and Shiva Aser B'Tammuz? They are only day time fasts. Why are more obligated in these fasts than say, the Mitzva of Tzitzis? They are both time bound, just day time Mitzvos.
The release for women from time-bound mitzvos applies only in principle to mitzvos that are positive time-bound mitzvos only.
“Time-bound mitzvos” means any mitzvo that has a specific time (or date) associated with it. So Tisha B'av and Yom Kippur are also time-bound.
Generally the mitzvo not to eat is a negative commandment and so fasts are, in principle, obligatory on women. But women do have reasons to be exempted as is explained in the linked question Why don't Israeli women fast? .
Up to this point was the first version of the answer. Now I add the following:
Fasting on Yom Kippur is a negative mitzvah as stated at www.etzion.org.il
התענית ביום הכיפורים מוגדרת (גם) כמצוות לא תעשה, ולכן נשים חייבות בה
and so women are obliged to fast on it.
Toras Emes states that the reason that women fast on the minor fasts is:
ארבעה צומות חייבים להתענות בי''ז בתמוז בתשעה באב ובג' בתשרי ובעשרה בטבת, מפני הדברים ההרעים שאירעו בהם.
Four fasts: Women are obliged to fast on 17 Tamuz, 9 Av, 3 Tishrei and 10 Teves because of the the bad things that happened on these dates.
The implication from the author giving this reason is that at least he views this reason as being stronger than the reason to fast is a negative mitzvo and possibly he holds that to fast on these days is not a negative mitzvo at all.
Acknowledgement to @mevaqesh for his points.
