In Othello, what is Cassio's relationship to Bianca in regards to the end of act 3?
Cassio and Bianca are at the very least seeing each other by the end of Act III. The difference between the two is their impression of how serious the relationship is. At this point in the text, Bianca finds a token in Cassio's room she thinks is from another woman. This happens to be the handkerchief that was purposely stashed there by Iago to stir up jealousy. This scene demonstrates he did not get the jealousy he was looking for, but certainly made Bianca think about who else Cassio might be seeing.
As they continue their discussion Cassio asks her to leave because he does not want Othello to see that Cassio can get distracted by a woman. It is almost as if Cassio views Bianca as if she is just a toy to play with for now.
They are a secret item, a potential boyfriend and girlfriend, but Bianca is into Cassio more than he is into her.