The best replacement for bebop is swing.

The best alternatives to bebop are rated as following:
★★★★★  swing
★★★★  cool jazz
★★  trigun
★★  samurai champloo
★★  hard bop
★  speedplay
★  outlaw star
★  jazz
  champloo
  black lagoon
  code geass
  swing music
  big band
  rocksteady
  bop
  d gray man
  firefly
  swing jazz

Your alternative for bebop is not listed? Suggest!
Speaking about bebop, one probably shouldn't forget about aesop.

Other search terms related to bebop and their ratings are:
★★★★★ aesop
You have in mind a companion for bebop and it is not yet here? Propose!



Google Trends

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bebop
swing
cool jazz