"The bag" can be either "el bolso" or "la bolsa" - is one preferred, or more common, than the other?
Is it that one is used in some circumstances, and the other in others?
English purse, Spanish bolsa, and French bourse all derive from Latin bursa. Just as there are many kinds of bag or sack, so too are there many kinds of bolsa and bolso.
For the most part, bolsa indicates a larger thing, such as the large shopping bags you take groceries home in, whereas bolso indicates a smaller handbag, pocketbook, or purse — or the smaller plastic bags at the supermarket. A bolsa can also be a bourse or stock exchange, while a bolsillo is normally the pocket of a garment.
In certain regions all this can be switched around. For example, in Mexico a bolsa is the pocket of your trousers where you stick change or your billfold or any other pocket on your clothing, whereas normally this is a bolsillo.
Bolsa is also a more general word used for various sorts of sacks and expressions, including medical terms. Tener algo como en la bursa is to have something in the bag, to have it all sewn up.