According to her Wikipedia article, this Isabel was the daughter of Karl Alfred, Duke of Croÿ, and his wife, Princess Ludmilla von Arenberg and should not be confused with Isabella von Croÿ or that Isabella's daughter Archduchess Isabella.
From eBay; spots removed with Photoshop and sepia tone removed. Also posted to The Belle Époque - 1890 to 1914 Album here.
Isabella Antonie wears a stylish trim silhoutte dress in this photo.
Isabella Antonie of Croÿ, Princess Franz of Bavaria, Prinzessin Isabella von Bayern, Prinzessin Franz von Bayern, Isabella Antonie Eleonore Natalie Klementine, Croÿ family, Wittelsbach family, Princess, German, bouffant coiffure, blouson bodice, scoop neckline, elbow length sleeves, ruffled cuffs, waist band, down turned waistline, close skirt, drapery, fur wrap