Bebop, also known as Bop, was a radical new style that developed in the early 1940's, and became popular by 1945.
With breakneck tempos, stunning extended solos and advanced harmonic sensibility Bebop made people sit up and take notice.
Technique will come into play here as tempos are pushed so high that the ride is not swung but played as straight eighths.
During a solo, the musicians will usually improvise around the chords, rather than staying within the boundaries of the melody.
Definitely check out it Charlie Parker and Dizzie Gillespie then try, Sonny Stitt, Bud Powell, Tadd Dameron and Barney Kessel.
For Big Band meets Bebop try Stan Kenton or Woody Herman.
Important: Feather the bass drum for all 4 beats, and play the high-hat with your left foot on beats 2 & 4. If the bass drum is notated with something different than quarter notes (comping), play the bass drum.