 "Bye Bye" received mostly positive reviews from music critics, and was heavily speculated to have become Carey's 19th number-one single on the Billboard Hot 100. Many reviewers complimented its simple and understated musical arrangement and personalized lyrics, while some felt the song was too simple for an artist of Carey's stature. Jeffrey Mitchell from The Hollywood Reporter described it as a "high point" on the album, and wrote "Mariah softly and sweetly lamenting the loss of any kind of loved one on the truly touching 'Bye Bye'. Mitchell concluded his review put stock in the song's success, and ended with" Thankfully, it looks like we won ’ t be saying “ bye ” to Mariah for a long time. "An anonymous journalist writing in for MTV UK called" Bye Bye "a" tear jerking ode to people who have passed away ", and assumed it would" have reality pop contestants singing away for decades to come! "The Houston Chronicle's Goey Guerra highlighted the song as" truly trademark Mimi ", and described it as" a lighters-and-hands-in-the-air tribute to deceased loved ones ". Dan Hinkley of Daily News branded it" the album's most potentially personal song ", and assured it would become Carey's 19th chart-topping single in the United States. The song received positive response from both Rolling Stone's Christian Hoard and Yahoo! Music writer Dann Gennoe, who describes the track as a" piano-based big-voiced "and" lighter-friendly " ballad. In his review of E = MC ², a writer from the Los Angeles Times described the song's lyrics and production in detail:
