Those belts with the little water bottles on them are usually called fuel belts, though that is actually the brand name of the first company to make such belts... Many companies make something similar now. I have been using my fuel belt for 10 years, I love it. It does not bounce, though it can sometimes chafe if your aren't careful.
I have a friend who used to carry a hand held water bottle. She was unable to get beyond 6 miles without major back pain. One day she ditched the bottle and had no pain whatsoever, even when running a half. The bottle doesn't weigh much and seems innocuous... But it will still change your posture and natural arm swing and might cause you issues.