Bolt had four hits including his third-inning blast to right center, while Tyler Ramirez added three and two RBIs on a night when the Tar Heels matched their season high in hits against the Runnin' Bulldogs (23-27).
Carolina (31-21) jumped out in front after just two batters as Michael Russell and Parks Jordan doubled off GWU starter Jeremy Walker (3-2). Ramirez made it 2-0 with an RBI single, and Bolt's line drive homer in the fourth pushed the Tar Heel advantage to 4-0.
Cherry (2-2), who won for the second time in as many starts, stranded seven runners in the first four innings before retiring seven straight over the middle innings. After two Gardner-Webb batters reached to lead off the seventh, Trevor Kelley replaced Cherry and escaped the jam without allowing a run.
Myers, who started at second after missing eight games with a broken fifth metacarpal in his right hand, drove in Carolina's fifth run with his second hit in the fifth against lefty Mitch Warner. The Tar Heels sent eight men to the plate in the ninth to add two insurance runs, with a Landon Lassiter single and a Ramirez double plating the final runs.
Kelley allowed a pair of runs in the ninth but got the final nine outs of the game to pick up his second save of the year.
J.J. Nazzaro, Ryan Hodge and Henry Rundio led Gardner-Webb's 10-hit attack with two hits apiece.
Cherry, who hadn't won since the 2013 ACC title game prior to last week's victory at Elon, scattered six hits and walked three over 6.0 scoreless frames. The sophomore righty struck out four and needed just 89 pitches to work into the seventh.
Carolina will now return to Chapel Hill before flying to south Florida Wednesday in advance of a three-game series at Miami Thursday-Saturday. Thursday night's opener is set to begin at 7:30 and will be televised by CSS. A live stream will be available courtesy of ESPN3 at WatchESPN.com.