There are actually three types of bebop scales. The first one is the bebop dominant scale. It uses both the major seventh and lowered seventh scale degrees. So, if you were in the key of C major, the scale would be:
C, D, E, F, G, A, Bb, B natural, C.
The major bebop scale uses a regular 5th scale degree and a raised 5th scale degree. So, in the key of C major, the scale would be:
C, D, E, F, G, G#, A, B, C.
The minor (Dorian) bebop scale uses a minor and a major third. So, in the key of C, the scale would be:
C, D, Eb, E natural, f, G, A , Bb, C.
These scales were used in the 1940's during the bebop era. Hope that this helps.
Jremon
