It failed to make the top 40 in either the United Kingdom (only reaching No. 56) or the US Billboard Hot 100. In the United States, the song reached No. 8 on the Hot Dance Music/Maxi-Singles Sales chart, but failed to chart on the Hot 100 during its original 1986 release. However, a new mix included on The Best of New Order was released in 1994 and finally made a brief appearance on the Billboard Hot 100 in the number 98 position in 1995.
The 12-inch version, remixed by Shep Pettibone, also appears on the compilation Substance and a second remix by Stephen Hague features on their Best Of album. The original album version appears on the 2005 compilation Singles, the 7-inch version appears on the 2016 reissue of this compilation. New Order's live versions since 1998 are based on the Shep Pettibone remix.
The single mix features a cleaner sound with more electronics than the album version, notably the Fairlight CMI music workstation, the premier sampling keyboard workstation of the '80s, used to provide novel sounds, such as the orchestral hits that were so popular, but also to sequence the song. All instruments except vocals and Peter Hook's melodic bass were sequenced (the song also prominently features synthesised bass and synth choir parts).
The music video, which was released in November 1986, was directed by American artist Robert Longo. It prominently featured shots of a man and a woman in business suits flying through the air as though propelled by trampolines; this is based directly on Longo's "Men in the Cities" series of lithographs. The video also features a black and white cut-scene where Jodi Long and E. Max Frye are arguing about reincarnation, in which Long emphatically declares "I don't believe in reincarnation because I refuse to come back as a bug or as a rabbit!" Frye responds, "You know, you're a real 'up' person," before the song resumes.
Australian band Frente! released an acoustic cover version of the song in 1994, re-imagining it as a folk ballad. Issued as part of the Lonely EP in their home country, the cover peaked at number seven on the ARIA Singles Chart and became the band's only overseas hit, reaching number 49 on the US Billboard Hot 100, number 53 in Canada, and number 76 in the United Kingdom. In Australia it came in at number 63 on the 1994 year-end chart and was certified Gold for shipments of over 35,000.
US editions mis-credit "Bizarre Dub Triangle" as "I Don't Care", reputedly due to a record company person contacting New Order's Manager Rob Gretton to ask what to name the mix as, Gretton is claimed to have said "I don't care"