If you want to add calcium then you don't want sodium bicarbonate. There is no Ca in it.
Do you also need to add magnesium? There are several GH boosters out there with balanced levels of Ca and Mg. Gotta read the label though, to make sure of everything that is in them.
Calcium chloride is another source of calcium that is just fine in aquariums.
Depending on what else is mixed with the calcium the pH may change, but this is not because of the calcium. It is because of the 'other' stuff, usually carbonate or bicarbonate, though other materials can also alter the pH.