This is my failproof method to make a successful ginger bug. The first time I made it, I ran into a lot of issues getting it started, but now it works every time.
Combine the water, ginger, and sugar in a mason jar. Stir vigorously until the sugar dissolves. Loosely cover with a lid, plastic wrap, or a paper towel with an elastic band. Store in a cool, dark place.
Feed your bug daily with one tablespoon of chopped ginger and one tablespoon of sugar. Make sure to stir vigorously each time until the sugar mostly dissolves.
By day 3, you should notice some bubbles sitting on top of the water. By day 5, you should see a steady stream of bubbles. The mixture should smell yeasty with a hint of ginger. If there are any bad smells like sulfur, eggs, or farts, then bacteria have taken over and you will need to restart.
Ginger Beer
Add ¼ cup of the ginger bug (make sure to stir it well beforehand) and 4 cups of fruit juice to a glass jar. Cover it loosely with a lid for 1-2 days until you see a steady stream of bubbles. Transfer the liquid to a plastic soda bottle or flip-top brewing bottle and close the lid tightly. Let it ferment for another 1-3 days, burping every 12 hours, until it reaches your desired level of carbonation. Then transfer to the fridge and consume within two weeks.