I read that hydration has a dramatic effect on oxygen absorption. Drink, drink, drink.

Also, check your iron level. Many women are anemic (I am) and this means their blood doesn't have as many red cells to bring oxygen to the working muscles. Result - you are gasping.

As for the rest, I agree, just do hills more and more. For me it was a sudden, magic day when I realized that I'd ridden all the way up a fire road that I'd always had to stop at least twice on just from shortness of breath.