Bags are a very old tool for carrying things in.
Bags were used by the ancient Egyptians and bags were used by the ancient Europeans. It may even have been so that these antique bags were made in line with somekind of ancient fashion but little is known of ancient women and their bags.
If you take into account the relative sophistication of the backpack that was on the body of the 5300 year old ice-man (Oetzi) found in Austria, it does not seem inconcievable that their women would have had the skill and creativity to create other bags too.
Bags in the middle ages
At the end of the middle ages there are a variety of bags for men as well as for women. There were metal frame-bags hanging from the belt except for bags that were used for hunting which were carried over the shoulder.
Bags during the renaissance
At the start of the renaissance men and women both wore bags but by the end of the 16th century bags became mostly the domain of women because of the introduction of pockets into men's clothing.