It’s a crowded Tuesday night at McGreevy’s when Steve Conine makes his debut behind the bar. After a crash course on how to pull a pint, the 38-year-old turns to take orders from the crowd. He musters up a rum and coke and a cosmopolitan, but freezes when someone orders something called a blazing roadrunner. Good thing he has a day job. Conine is not in training to be the mixologist of the moment, he’s treating his staff - from online shopping company Wayfair - to some holiday cheer and raising money to boot. No longer stuffy affairs defined by chicken dinners, award presentations, and small talk with the guys from accounting, some holiday parties have a new twist - bring your own bartender. As cocktail-making reaches gourmet status, bars and bistros across the city are adding drink demonstrations and tutorials to their party offerings, some featuring company brass behind the bar. “We are not just showing employees we can rent a ballroom and get a DJ,’’ said Michelle Lemire, Wayfair’s learning and development manager who booked the holiday party earlier this month at the lively Back Bay bar. “In this economy, companies want to do something lower key, but also have a good impact.’’