The reason the balloon will burst is because there isn't anywhere else for the gas to go as long as there's a tight enough seal to keep the balloon on the bottle. The human stomach has two valves to control the pressure which would build up. When the gas builds up, you're either going to burp or the gas will travel through the rest of the digestive system and you'll "pass gas".
As Hyp mentioned, they tested this on Mythbusters. It took pounds of Pop Rocks and gallons of soda to get a pigs stomach to explode. First, I doubt anyone would consume that much of either at any one time. And second, they had a sealed system which did not allow the gas to exit either end as would normally happen.