With all due respect to Mssr. Bouguereau (who is obviously very talented), his Miss Gardner looks green, goulish, and ghastly to me.
I understand that if there are cool colored surfaces in the environment, highlights will tend to be cool colored; but any green will be brought out in contrast with the reds of the fleshtones.
Miss Gardener's green almost looks like a yellowing of the oil over a bluish shadow (although the white is pretty white and not yellowed, so that's probably not the case).
"Maternal Adoration", on page 3 of the Bougereau site, and "Seated Bather", on page 2 of the site, show blue shadows of the type I don't like -- the bather looks positively corpselike.
The example that always comes to mind is the neck of Helen in the classic work "The Abduction of Helen" by Guido Reni...
http://www.calliope.free-online.co.uk/abduct/pic20.htm
...I've got an even better picture at home, in my little book "Treasures of the Louvre", and the neck looks like it is made of steel, compared to the alabaster face and rosy cheeks of the lady.
I've seen paintings by Masters that were not completed; and in the unglazed areas, the underpaintings show through the same -- blue-black-gray shadows -- not an effect of an under layer becoming more visible as an upper layer becomes more transparent over time ("Pentimento", Italian for "repentance").
Fortunately, many underpaintings were done with white and burnt umber, for more "organic" shadows. The only bluish shadows I've seen on actual human beings have been in black beards of men or in rooms with blue walls.
To me, blue shadows on flesh are the realm of abstract art -- in which primary colors, not subtle tints, tones, and shades, are more the rule.