BAD-girl rapper Eve celebrated the completion of 45 days of sobriety by hitting the bar. The songstress was freed from her alcohol-monitoring anklet on Saturday morning, and by cocktail hour was hitting the MTV Video Music Awards swag suites at Caesars Palace. “When a cocktail waitress walked over to her with a bottle of Svedka, her eyes lit up,” said a Page Six spy. “She got kind of nervous when they wanted her to take a photo, and wouldn’t pose with the bottle – but then her assistant asked a promoter to send a case to her house.”