Bottom, in Midsummer Night’s Dream, has suggested that he play the part of Pyramus in a “French-crowne colour’d beard, your perfect yellow,” and Quince replies, “Some of your French Crownes haue no haire at all, and then you will play bare-fac’d.”
The meaning is thus clear, “having no hair upon the face, beardless.”
Because it is the stripling or boy who is beardless, and because the stripling or boy is usually bold, impudent, shameless, or audacious, the latter is now the usual use.
For example, Dickens has the beadle, Mr. Bumble, say to Oliver Twist, who pleads not to be apprenticed into the “chimbley-sweepin’ bisness,” “Well, of all the artful and designing orphans that ever I see, Oliver, you are one of the most bare-facedest.”