Caretaker boss Lee Carsley, who assumed control following Robins' departure to Huddersfield on Thursday, savoured victory thanks to goals from Leon Clarke and Carl Baker.
Coventry were ahead inside three minutes, Clarke shrugging off a challenge from Ashley Eastham before rifling a powerful finish through Trevor Carson's legs.
The Sky Blues kept up the pressure and Stephen Elliott blasted against a post while James Bailey was denied on the line by Joe Skarz.
Bury saw chances limited but David Worrall tested Joe Murphy with an impressive piece of skill, taking down a Skarz pass to hit a stinging volley.
Andy Bishop also missed a superb chance to equalise, allowing his effort to be deflected wide after dwelling too long inside the box.
Carson denied both Gary McSheffrey and Clarke after the break but Baker extended his side's lead with a low finish from 20 yards.
Richard Wood ensured a clean sheet by clearing Nick Ajose's late effort off the line.