A purse carries far more than your personal belongings -- cigarette smoke odors linger in the bag long after you leave a smoky environment. Instead of bypassing that purse for another just because of the smell, remove the foul odor with natural odor-eating treatments and a healthy serving of fresh air.
Open all compartments in the purse and remove all the contents. Porous items kept within the purse may hold the smoke odor as well, and should be aired out before you put them back in the purse. Tug at the linings within the pockets and pull them outward, if possible. This helps air out areas that normally do not receive much exposure to fresh air.
Set the open purse outdoors for several hours, ideally on a non-humid, breezy day, to help air out some of the smoke scent. If the bag is soft and pliable enough to turn inside out, do so to allow it to freshen outdoors for a few more hours.
Wipe down the inside and outside of the purse with a mixture of equal parts white vinegar and water. Wet a soft white cloth with the liquid until it is damp but not wringing wet to avoid damaging materials such as leather. Flip the bag onto its side and wipe down the bottom and purse handles or straps as well. Let the material dry completely.
Sprinkle baking soda inside the purse, including all compartments and pockets. Close the compartments and stash the bag in a non-humid environment for a day or two, and then dump out the baking soda. Wipe excess baking soda away with a dry or slightly damp cloth.
Place a sheet of plain copy paper inside the purse if it still smells smoky. Pour ground coffee on top of the paper, and then wad up several more sheets of paper and stuff them inside the purse. Close the purse and place it in a non-humid location, ideally outdoors, for two or three more days. Replace the paper and ground coffee each day. Both the paper and coffee absorb odors, and the coffee smell goes away on its own.