Even though the drama is full of verbal deception, physical disguise only happens twice. First is when masked Bosola tries to capture the Duchess. Second is when Bosola disguises himself as an old man to strangle the Duchess. Is there significant difference in two ways of disguise? Also why he dressed up as an old man?

In the first case, when Bosola tries to capture the Duchess, he's wearing a mask. This is a sign that he's simply carrying out Ferdinand's orders. He personally has come to admire the Duchess for the remarkable fortitude she has so graciously displayed in the midst of all her various troubles. But at the same time, he still remains a loyal, faithful servant to his master. Bosola's wearing of the mask is his way of distancing himself from a deed he finds especially disagreeable.
Much the same rationale is behind Bosola's disguised appearance in Act III. Here Bosola enters, disguised as an old man, and tells the Duchess that he's come to measure her for a tomb. Once again, Bosola has been given a very unpleasant duty to carry out by Ferdinand; and once again he does as he's told. But, as previously, he's adopted a disguise as a way of trying to reconcile his growing admiration of the Duchess with his professed loyalty to Ferdinand.