David Baker was the first one to come up with the term 'Bebop Scale' in his book 'How to Play Bebop', describing a technique Charlie Parker and C° used to make those long, never ending bebop lines. Today it's almost unthinkable for a jazz musician to not at least speak a bit of the bebop language and the bebop scale is a good place to get you started.
The Bebop Scale is a Myxolydian Scale with a descending chromatic note between the root and the b7.
This G Mixolydian scale is the V of the C major scale. The G Bebop Scale can be played on most chords that are diatonic to the key of C major, but not on the C major chord itself because the F is an avoid note for the C major chord.
The Bebop Scale is a dominant scale and has the same function in a key as the Mixolydian scale. It can be played on the dominant and the sub dominant. Our example, the G Bebop Scale, is the dominant of C Major and can be played over G7 and Dm7, giving us a great tool to play over II V I progressions.
You can also play the bebop scale on half-diminished chords. The G bebop scale can be played over a Bm7b5 chord.
The Bebop Scale works best descending.
The advantages of the Bebop Scale :
Here is the G Bebop Scale on the fret board :
: represents the root or 1 of the guitar scale.
: represents a guitar scale note.
These two positions are the basic positions and are the best to get you started. Needles to say you can play the bebop scale in any position you want.