I own a white marble statuary bust that is yellow and dingy-looking. What can I use to brighten it up?

Old marble sculptures can be made out of marbles that contain iron. Over time, the iron becomes oxidized and turns yellow. If the yellowing you are observing is the result of iron staining, it cannot be removed. If the yellow is only surface dirt, try cleaning the bust with a solution of stone soap or neutral cleaner. A soft toothbrush can be used to get into all the nooks and crannies.