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She ran against Mr. Burns in a governor's election, winning a landslide after Marge served Mr. Burns a three eyed fish, which he promptly spat out even though he said it had a taste that can't be beat.
She also judged Bart and Lisa's class projects (designing a new State flag), in Capital City. She yells in disgust after unfurling Lisa's flag, which Bart had redesigned to make it look like a butt with "Learn to Fart" underneath.
Bailey also brings order amongst the prisoners in a jail riot and pardons them. She was also present at the 38th Annual Springfield Media Awards.
 Governmental Position
Given Mr. Burns' membership in the Republican Party, Bailey is presumably a Democrat, although that has never been stated and she could also be independent of political parties. Governor Bailey ordered an investigation about possible pollution by the Springfield Nuclear Power Plant. The investigation did not find anything on pollution, but did find that the plant was not up to code.