HCO3- + H+ -> <- H2CO3

What would happen to the body's acidity if additional HCO3- was given to a patient? (see equation above)

Have you heard about Le Chatelier's Principle?

Along the big lines, it states that a reaction in equilibrium will oppose any change that is applied to it.

So, if you add more HCO3-, the equilibrium will shift so as to decrease the amount of HCO3-. What do you think will happen to the amount of H+ (which accounts for acidity)? :)