Bald-faced refers to a clean-shaven face or a feature that is figuratively clean; barefaced means the same but also refers to a face unobstructed by a mask; boldface only refers to thickened letters, often used for emphasis in writing. Mountains free of vegetation may be bald-faced or barefaced, a criminal who forgot his mask is barefaced, and a font thickened for emphasis is boldface.
When it comes to dishonesty, brazen lies were traditionally only barefaced, but since the early 2000s, bald-faced lie has exploded in popularity in American English, surpassing the use of barefaced lie by around 2010. British English still largely prefers the historically-consistent barefaced lie, but both may be considered acceptable.