Looking back on ancient history, it is tough to find any real proof that women were skilled in archery, except for one group that keeps popping up - the Amazons. The Amazons were a nation of all-female warriors in Greek and Classical antiquity. Amazons were first depicted in art around the 8th century, and in writing around the same time (or later) in Homer's Iliad, in scenes concerning the Trojan War.
In the 5th Century BC, the poet Pindar describes the Amazons as horse-riding female archers. Strabo (a 1st Century Greek historian and philosopher) speaks of the Amazons having their right breast "cauterized at a tender age" (source) to more easily throw spears, and so that a bow could more easily be drawn (although this is questionable, unless they were left-handed) - Hippocrates also mentions the missing breast trend.
Also included in Greek Mythology is the female archer Atalanta, and the goddess Artemis (Roman equivalent, Diana) - goddess of the hunt, wilderness, wild animals and virginity. One of her epithets was "of the golden shaft", another, "arrow-pouring" (and another, "mistress of the beasts" is pretty cool too) and the image of a golden (or silver?) bow and arrows is symbolic of her. According to Greek Mythology, Artemis' father, Zeus (you may have heard of him...), asked his daughter what she desired in the whole world, to which she responded that she would have a bow and arrows, a pack of hounds to hunt with, nymphs to accompany her, a tunic short enough for her to run in, mountains and wilderness as her own special places, and eternal chastity (isn't chastity one of the first things that pops into every three year old's mind when asked what they want?). And so, Zeus granted it, and she went beneath the sea to Cyclopes to forge her silver bow and arrows. And once she had collected her nymphs, and got her hounds from Pan (as you do), she couldn't wait to try out her bow, and so hunted by torchlight.
Dianna of Versailles - a first century marble statue of the goddess Diana (Greek: Artemis)
Returning somewhat closer to home, we have Skaði, a Norse goddess associated with winter, mountains, skiing (this brings pretty funny images to mind) and.... bowhunting! In all sources (Poetic Edda, Prose Edda, and more) Skaði, daughter of Þjazi, marries the god Njörðr as compensation provided by the gods for killing her father. In the Prose Edda, the figure of 'High' tells the story of how Skaði and Njörðr go their seperate ways due to him wanting to live by the sea, and her wanting to live in the mountains. High then mentions that Skaði returns to the mountains where she skis, wields a bow, and shoots wild animals, while Njörðr goes on to have two children, Freyr and Freyja.
Njörðr and Skaði on the way to Nóatún (1882) by Friedrich Wilhelm Heine
Oh ya know, just skiing and throwin' spears, the usual
As you can see, Skaði can draw a bow with both tits intact