First, realism as a movement and realism as a style are two distinctly different things. Realism in the latter sense is also referred to as naturalism, mimesis, or illusionism and is found in many time periods as a matter of technique and training. It became especially marked in European painting by artists in the 15th century. Since realism is not only prevalent in the era of Julius Caesar it is possible that the bust was created by another sculptor.
Also, while the hair of the bust is the same as the image on coins, the nose is different. If the nose and coin had been made by the same person