Initial reviews toward "Some Kind of Bliss" were mixed. Writing for
NME in November 1997, Ben Willmott called it "supremely irritating" and stated "Kylie belts out the lyrics like she's reading from an autocue. Any soul is lost in a slurry of bought-in brass and a ropey guitar solo that's be more at home on a
Shakin' Stevens record." John Magnan from
The Age said while the song was a stand out to the album, it "is actually one of the album's clunkier tracks". A reviewer from
Music Week awarded the song four stars out of five, stating "Kylie changes musical tack again with this dense, big sounding single, co-written with two of the Manics, which loudly announces she's back in style." Gareth Gorman said that while the song showcased Minogue's "thin vocals", he followed saying "it still works due to one of those melody lines that is inevitable stunning, simple and effective." The song received more positive reviews in retrospect.
Allmusic's Chris True had selected the song as an album stand out and a career stand out track. While reviewing her 2002 compilation
Confide in Me, True stated “
Impossible Princess, both of which found her stretching and growing beyond the pop princess image she had previously. Dark, noisy tracks like "Limbo," the trip-hoppy "Jump," and the more rock-oriented "I Don't Need Anyone" and "Some Kind of Bliss"—both of which were co-written by the Manic Street Preachers' James Dean Bradfield—found her trying on different styles to replace the
bubblegum pop of the past". A reviewer from
Who Magazine called the song "Funky , Spunky, Rocky, Big." Matt James from
PopMatters reviewed her compilation
The Best of Kylie Minogue and was disappointed with "Some Kind of Bliss"' absence, labelling it a "lost classic". In 2017,
Billboard ranked it as the 76th greatest pop song of 1997; Andrew Unterberger wrote that "the song's string-soaked guitar-pop remains surprisingly alluring, a fascinating glimpse at an alternate reality in which the disco diva is better remembered for ripped jeans than golden hot pants, and sounds no less like herself for it". Writing for the
Herald Sun, Cameron Adams placed it at number 21 on his list of the singer's best songs in honour of her 50th birthday, calling it "the peak of 'Indie Kylie' [...] a modern retro '60s girl band garage pop heaven, filled with brass, sass and class". ==Chart performance==