
Bianca functions as the unwitting third point of the handkerchief's journey, her genuine jealousy over Cassio providing Iago with a final, visible piece of 'evidence' to present to Othello. Her wrongful accusation after the attack on Cassio extends the plot's collateral damage to a character who never has any stake in the main tragedy.
Bianca is a courtesan in Cyprus and Cassio's occasional lover, introduced partway through the play as a woman genuinely fond of Cassio despite his casual, sometimes dismissive treatment of her. Her jealousy when he asks her to copy the embroidery on an unfamiliar handkerchief — Desdemona's, though she has no way of knowing it — is rooted in an entirely reasonable suspicion that Cassio has another woman, a suspicion that is, in its own small way, as misdirected as Othello's much larger one.
That handkerchief becomes, through no design of her own, a piece of evidence in Iago's plot: when she returns it to Cassio in public, in view of Othello and Iago, her visible jealousy and the physical fact of the handkerchief in Cassio's possession appear to Othello as damning proof of Desdemona's affair. Bianca has no idea she has been made an unwitting instrument in a scheme to destroy a marriage.
Her final appearance, in the dark aftermath of the attack on Cassio, sees her accused by Iago of complicity in the attempted murder, purely as a convenient way to deflect suspicion from himself. Bianca disappears from the play under that unresolved cloud of accusation, one more minor life left disordered by Iago's manipulations without ever fully understanding why.
Bianca is motivated by real affection for Cassio and by a reasonable, if unwittingly consequential, jealousy over signs of another woman in his life — a jealousy that, unbeknownst to her, plays directly into Iago's hands.
Bianca's jealousy is drawn with a sympathy the play rarely extends to a courtesan character, presenting her as a woman with genuine feeling for a man who does not fully return the seriousness of her attachment. Her indignant reaction to the handkerchief is entirely understandable on its own terms, which is precisely what makes her so useful, and so blameless, as an unwitting piece of Iago's design.