For the most part, women’s clothing isn’t unlike the men’s. They often wore a basic tunic with more decorative outer garments, or a modified version. In Jewel of Persia I usually dress my heroine in a simple Greek chiton, as seen on the cover and in photos. It’s just two panels of cloth, sewn up the sides until the torso area, which becomes the armholes. It’s then fastened at the neck and shoulder to create a sleeve. It’s belted to create a defined waist.
But those with wealth would also have access to the fashions of the vast empire, including the sheer linens used by Egyptians, close-fitting sheaths for underneath, and more complicated, draping styles. Kasia prefers simplicity, so other than when she is presented to the king, her garments are always described as unadorned and modest. Others covered the garments in jewels and embroidered them with gold and silver. Esther would have been resplendent in her finery–though of course, tasteful. 
Though in all likelihood they would have worn head coverings to protect from the sun outside, I didn’t find anything saying this was a must.