In Act 3, Scene 5, Bosola visits the Duchess with a mask on. What is the symbolization of this mask? I personally think that there is no need for Bosola to hide his identity. He have already gotten the duchess. Then why is he wearing a mask?

Bosola is a spy and so used to playing a part. When he comes to arrest the Duchess, with a troop of masked horsemen, that's effectively what he's doing. Earlier in the scene, when he brought supposedly glad tidings from Ferdinand, he could do so as himself, as the real Bosola. But now, when he comes to arrest the Duchess, he is acting solely as the voice of Ferdinand. Wearing the mask is Bosola's way of trying to resolve his internal conflict as he's constantly torn between contradictory impulses. On the one hand, he wants to be a loyal servant to Ferdinand; but at the same time, he admires the dignified, stoical way that the Duchess conducts herself despite all her troubles.
In wearing the mask, Bosola is trying to separate himself from the dirty deed of arresting someone he's come to admire. It's noticeable that, in this scene, Bosola speaks in short, clipped sentences. He's almost turned into Ferdinand's automaton as he tries to distance himself from the unpleasant duty he's been ordered to carry out.