It would be a simple matter of just tossing your fragrance in your bag and reapplying as needed, if the bottle wasn't usually glass and fragile. A common trick is to spray the perfume onto a cotton ball, store the ball in a sealable plastic bag, and squeezing out as much air as possible from the bag.
Now, when you need to reapply, just grab your scented (and still moist) cotton ball and apply.