It certainly could be her swallowing a lot of air as she rushes to drink the water and I completely agree with the suggestions of limiting how much she can drink at one time. That's the perfect place to start to resolve the problem.

If you try the rock in the water bowl and she still seems to be experiencing the burping, there may be a problem with the water actually reaching her stomach.

Does she physically retch to bring the water up, or does the 'burping' seem quite easy for her to do?

Has she brought up any food recently too?

As pit bulls are sadly a banned breed over here in the UK, I don't have a lot of knowledge on how prevalent oesophageal conditions are in that breed. Your vet ought to investigate this further if the problem persists. There are several ways that this can be done, ranging from a simple examination in the surgery to an X-ray of her neck and chest, but your vet will of course advise what is best. It might be worth investing in a blood test at the next vet visit, too, just to check if there's anything underlying that may be making her more thirsty than normal.

These suggestions are of course just that, suggestions, and she may be perfectly healthy internally. It's just best to check these things, and to ensure that your vet is checking all possible avenues too!