A turn of phrase coined by Inetta the Mood-Setter, a part-time DJ from WBLX-FM 92.9. After being treated like crap by the radio station and people at the station for years and then getting a shit raise, she quit on the air. She refused to take it anymore and said on air: "I QUIT THIS BITCH!"
It is a term generally used to show extreme disgruntlement with a work position or used more casually at the end of the work day to denote that you are not working anymore after that point.
After being forced to work 70 hours a week with no overtime and no hope of compensation or recognition, Bob walked into his bosses office, flipped him the bird and said: "I quit this bitch!"