Can baking soda dissolve in water?

Yes, they do make a chemical reaction. It sort of 'fizzes' as carbon dioxide is released from the sodium bicarbonate (baking soda). The sodium mixes with the acetic acid (vinegar) to form sodium acetate which is a salt soluble in the water that makes up most of the vinegar which is why you can't see much chnage once the fizzing stops. If you tast vinegar, it is sharp, all acids are sharp to taste. If you taste the baking soda it is very bitter. If you use a tiny amount of vinegar and lots of baking soda and taste the liquid left after the reaction has stopped (no more fizz) the sharp acid taste of the vinegar will have lessened and been replaced by a sort of salty taste.