While "bodega" is the Spanish word for "wine cellar" or "storeroom," and is used in Spanish-speaking areas to describe small grocery stores or convenience stores, it's not commonly used by Mexicans themselves to refer to stores in the same way as it is in some US cities like New York.
In Mexico, a small grocery store or convenience store would typically be referred to as a "tienda," "tienda de abarrotes," or a "tienda de conveniencia" (grocery store or convenience store)