The first thing that you should know is that it's fine to reuse tea bags. The drawback is that after the first cup, you lose flavor and strength. But if you enjoy strong tea, there is a way to reuse your tea bags.
First of all, you'll need to store the tea bag in a moist medium. Once they get dried out, they become a breeding ground for mold and bacteria. So your best bet is to store them in a small shot glass filled with water. That will keep them seeping while they are being stored. While you can leave them out in your kitchen, I usually put them in the fridge so that there is less chance of bacteria growth. If you think you've got bacteria or mold in your tea bag, the best indicator is smell. If it smells funky, trash it. A tea bag can be reused one or two times. After that, it's spent. Reusing green or white tea works better than darker blends. I usually reuse Orange Pekoe tea bags because I use two bags in one cup: I like strong milk tea in the mornings, with milk, no sugar. Once I've infused a cup, I'll keep the tea bags for my next cup. Then, I'll infuse both bags again with one new tea bag. The resulting second cup of tea is only slightly less strong than my usual cup, but perfect for the afternoons when I don't need too much caffeine. Reusing tea bags is best reserved for tea drinkers who drink a few cups a day, otherwise keeping the tea bags becomes an issue. [images via Leaf and Bean, Natural Family World, Lifehackery, Wikipedia]