It's true that Bartley doesn't know everything, but he knew enough to be very scared about it. He doesn't need to see the whole picture to be repulsed at whatever was being asked of him and his lackeys.
I suppose Schneizel could turn out to have a Geass or be given one at the last minute, but so much has been made of LeLouch opposing his father that I don't think they'll put it aside. So far Schneizel has been portrayed as the last great obstacle for LeLouch to defeat before he can realize his ultimate goal (i.e. defeating Charles), but so far as we've seen they have no hostile history and LeLouch has no specific vendetta or hatred against him. He knows he has information about his mother's murder, but that's all.
Also, Charles and V.V. are basically symmetry against the partnership of LeLouch and C.C. Much is starting to be made of this connection between V.V. and Charles. In contrast, for all we know Schneizel doesn't even know that V.V. exists.