David Baker, one of the world's finest jazz educators, named these scales the "bebop scales" because they were used so often by jazz artists from the Bebop Era. These artists include Charlie Christian, Charlie Parker, Lester Young, and Dizzy Gillespie, to name a few.-- Corey Christiansen, 
There are five types of frequently used bebop scales: the bebop dominant scale, the bebop Dorian scale, the bebop major scale, the bebop melodic minor scale and the bebop harmonic minor scale. Each of these scales has an extra chromatic passing tone. In general, bebop scales consist of traditional scales with an added passing tone placed such that when the scale is begun on a chord tone and on the downbeat, all other chord tones will also fall on downbeats, with the remaining tones in the scale occurring on the upbeat (given that the scale is played ascending or descending; i.e., no intervallic skips are played). As such, many heptatonic scales may be modified by the addition of an eighth passing tone to accomplish this same effect; however, the modifier "bebop" is reserved to indicate those scales most frequently used--and popularized--during the bebop era (and/or by modern practitioners of the bebop genre).
The bebop dominant scale is derived from the Mixolydian mode and has a chromatic passing tone between the 7th and the root. It has all the notes in both the major scale and the Mixolydian scale of the same root. This scale is often used over dominant 7th chords and all extended dominant chords, and the ii V chord progressions. "When someone says they're playing 'the bebop scale,' this is the one they're talking about."
The bebop Dorian scale (also known as the bebop Minor scale) is derived from the Dorian mode and has a chromatic passing tone between the minor 3rd and the perfect 4th. It has all the notes in both the Dorian scale and the Mixolydian scale of the same root. It is the 5th mode of the bebop dominant scale.
A second spelling of the bebop Dorian scale features a major seventh bebop note between the dominant seventh and the tonic instead of the more traditional major third between the minor third and the perfect fourth. The second style, featuring the major seventh, is generally used by guitar players for its accessibility when applied to traditional minor scale shapes (that is, it is simply easier for guitarists to play). However, many players and resources adhere to the traditional spelling of the scale.
The bebop melodic minor scale is derived from the ascending form of the melodic minor scale and has a chromatic passing tone between the 5th and 6th notes. It has all the notes of both the ascending form of the melodic minor (a.k.a. the Jazz Minor) and the Harmonic Minor of the same root. This scale is often used over minor 6th chords.
These scales are listed in David N. Baker's books on Bebop.
They are also included, with the exception of the Dorian bebop scale, in Roni Ben-Hur's book Talk Jazz: A Comprehensive Collection of Bebop Studies, which is derived from the work of Barry Harris. Ben-Hur further elaborates on the concept of placing additional chromatic passing tones between other notes in the scales.
The bebop harmonic minor scale is derived from the harmonic minor scale and has a chromatic passing tone (an additional ?7) between the 6th and the 7th notes. It contains all of the notes of both the Harmonic Minor and the Natural Minor (Aeolian) of the same root. It can be used on all three chords of a minor II-V-I progression. This scale is listed in Randy Halberstad's book Metaphors For The Musician--Perspectives from a Jazz Pianist. The Bebop Harmonic Minor scale is a mode of the Bebop Major scale; and is also known as the Bebop Natural Minor scale (as listed in Mark Levine's The Drop 2 Book).