In an iTunes podcast about "The World Without," Sudol revealed that she felt Bomb in a Birdcage is about "two totally messed up people trying to stay afloat despite all the odds."

"[5] Andrew Leahey of AllMusic gave the album four of five stars, calling it "a lively piece of work" and concluded that Bomb in a Birdcage is "a fitting display of the explosives this songbird now has in her arsenal.

"[4] Mackenzie Wilson of Bust magazine noted that "simple pop moments such as "What I Wouldn't Do" and "Happier" showcase [Sudol's] songwriting chops as well as her artistic confidence.

James Shotwell of Under the Gun Review called the album "beautiful and moving" and praised Sudol's ability to "[walk] the fine line between simplistic and lush.

"[8] On mxdwn.com, Charlee Redman called Bomb in a Birdcage "pretty pop with an edge" and "a pleasant listen, and maybe a sign of new directions to come.