Just as with your kitchen sink, you should practice preventative maintenance with your bathroom sink and shower. Once a week, lift the drain cover in your tub and use a cotton swab to remove the hair that has accumulated there. Then pour 1/2 cup baking soda followed by 1 cup vinegar down the drain. Let this sit for 20 minutes, then flush the drain with very hot water. To help keep your tub drain unclogged, buy a plastic or rubber hair strainer; simply place it over your drain and let it do the icky work for you.
If your sink or shower has developed hard-water or mineral deposits, you can get rid of them by soaking paper towels in undiluted vinegar and placing the towels over the stained areas. Let them sit for one hour and then wipe the areas with a damp sponge.