Sodium Bicarbonate is a soda, not a base.

Presumably adding acetic acid to the mixture could cause it to react to that in the bottle, and then the gas perhaps bubble out, rather than react later with your stomach acid.

But I don't think that's why people do it - more for tart taste. A spash of red wine vinegar (optionally with some sodium and potassium salts) in a glass then filled with water makes are rather enjoyable concoction.

(But taste is a personal thing... if I recall when I finally got around to trying it, the Joy of Cooking's claim that balsamic vinegar is "exquisite" on vanilla ice cream was not one I felt inclined to endorse... either that or I didn't pay enough for the vinegar)