The band started as a creation of Jeff. Hyperbubble first appeared as the attributed author of a track on the 1997 album Acid Ranch 2000. Several years later, Jess joined him after the dissolution of Pink Filth to re-launch the concept band. In 2004, Hyperbubble debuted their first album, Sol!d Pop. Described as "peppy synth pop par excellence" with "good humorous songs," the album showcased their ability to apply "the breakneck pace of punk… to straight-up synthpop," altogether self-described as "bionic bubblepunk."
Their performances contained a wry sci-fi element. The band was described as one "in the proud tradition... of musicians pretending to be robots," but "taking the android artifice to intentionally over-the-top extremes, then undercutting all the sci-fi hokum with flashes of genuine humanity." Sol!d Pop also displayed their persistent use of sampling; the band's most popular downloaded song, "Leon", even featured sounds from their cat. With their penchant for mixing, a remix version of the album soon followed. This tradition continued for future albums as well.
Hyperbubble realized regional success with a showcase band slot at the South by Southwest Music Festival and their 2007 album, Airbrushed Alibis, named a best local album. The band was later voted Best Electronica Band in 2008 and runner-up Best Electronic Band in 2009 and Best Electronic Act in 2010 in the San Antonio Current. They gained international recognition with recordings released by UK label Filthy Little Angels, which included Airbrushed Alibis. The "retro-techno-bubblegum pop" album continued their "cartoonish, Hanna-Barbera view of the future, informed by 1960s visions of the 21st century as an era of flying cars and robotic romance." A 2008 dub version of the album heavily remixed and slowed down the pace of the original tracks.
Huw Stephens featured the Hyperbubble song "Supermarket Casanova" on his nationally syndicated BBC Radio 1 program in 2007. Their tour of the UK the next year led to them being signed by Glasgow-based Bubblegum Records. Their first EP with the label featured a collaboration with Welsh bubblegum pop punk rocker Helen Love in which they covered her song, "Better Set Your Phasers to Stun", with an added vocal track provided by her. The release completed their transition to a truly international group.
Their next full-length CD, Candy Apple Daydreams, was described as a "cartoon automaton symphony" and a "pop opera… utilizing an amazing overture theme that weaves in and out of the entire album." The music "sounds something like Madonna would sound...if her music were geared more towards school kids." The effort hit several best-of lists, including popular Scot Spotify blogger the Pansentient League's top five synthpop albums, Electro and Pop's Top Albums of 2010 (France) and Favorite Albums Of 2010 by the Houston Press, which also dubbed it "the best electronic album to come out of Texas since Asmodeus X's Morningstar." The title track further made the English Electricity Club's top 30 songs of the year.
Releases in 2011 included their LP, Drastic Cinematic with the German label, Pure Pop For Now People. Characterized as a soundtrack to an imaginary Jean Luc-Godard film, the album possesses a darker and more atmospheric mood than their previous efforts. Manda Rin of the Scottish band Bis contributed guest vocals along with sampled sounds from her cat, Akiko. An extended CD/MP3 version from Bubblegum notably adds a remix of their song "Welcome to Infinity" by Mark Towns, who previously worked on Hits! The Very Best of Erasure.