This is really good to take the stinging sensation away and also reduce the swelling in the bite:
Make a poultice using baking soda and water; make the texture almost like wet sand. Just dab it on the bite and make sure that a good mound of it sticks to your skin. You can use this as often as you like, as there's no chemicals to worry about. You can also make yourself a cool-to warmish bath with a good shake or two of the baking soda; you want to be able to feel the soda in the water. Rest in the bath as long as you like and then shower off the residue. This is good for any itchy, "rashy" type stuff on your skin.