Gold usually is stamped to indicate its purity, so check for marks on the inside of the bracelet.
You can test gold at home with white vinegar. If you apply it directly to the metal and it changes its colour, then it is most likely not real gold. Equally, gold is a heavy metal, so if you place your bracelet into a body of water, it should sink to the bottom. Fake gold can also leave green tint marks on the skin, so check for any discolouration when you remove the bracelet.