Mrs. Corney is cautious, distrustful, cruel, and power-hungry. We first meet her when she’s fixing herself tea in her snug little room on a blustery winter’s day. The snugness of her little room is in sharp contrast to the bitterness of the rest of the workhouse, where the paupers have to live. She feels sorry for herself, though, despite the snugness, because she’s a widow, and kind of lonely.
When Mr. Bumble arrives to flirt with her and then to propose, Dickens keeps us from feeling at all sympathetic by satirizing her—he repeatedly refers to her as a "discreet matron," meaning that she won’t allow anything improper to happen with Mr. Bumble. But "discreet" also means that she won’t commit to anything without knowing what she’s getting into. She’s certainly "discreet" in that sense. Dickens uses her to satirize the workhouse system that was run by people more interested in taking care of themselves than of the poor.