The “woman in white” whom we see in the Pincio Gardens during the Punch and Judy Show is almost certainly a high class Roman prostitute (or courtesan, if you prefer). The speculation in class that she is Winterbourne’s “foreign lady… older than himself” from Geneva is highly implausible: she is alone and unchaperoned, exposed to view in a public park.
Peggy McCormack’s article says: “This woman very deliberately attracts Winterbourne’s glance in a clearly suggestive manner.” And Winterbourne obviously doesn’t know her, when he meets her glance, he looks away, he’s not interested. McCormack goes on to say that this encounter causes Winterbourne to doubt Daisy’s innocence again, but I’m not sure she’s right about that, though it’s possible. My own view would be that we are to take in the contrast between the openly flirtatious girl dressed in white with her innocent delight in the puppet show, and the slyly suggestive posture of the courtesan who is also dressed in white.