According to the title, it is a parody of "Bye Bye Bye" by *NSYNC. Joey Fatone also appears in this episode.
Joey Vitola tries to get Miley, Lily, and Oliver to leave, and he says "Bye, Bye, Bye," which is a line from an *NSYNC song, the band that actor Joey Fatone was a member.
As Jackson comments about Joey Vitola not being good even if he wore a "Justin Timberlake mask," it is a particularly cutting insult because the actor, Joey Fatone, is a former member of *NSYNC, with Justin Timberlake.
One particular scene shows actor Joey Fatone spontaneously beginning to dance on top of a restaurant table. Additionally, this references his former group, 'N Sync, who were known for their choreographed dance moves.
Joey Fatone and Jason Earles are the same age.