The bebop scale is a very handy scale to be familiar with for improvising and also it’s great to have under your fingers for big band and jazz charts that make use of this scale in their melodies.
The bebop scale fits over a dominant chord and places all the chord tones 1, 3, 5, and dominant 7 on the beat. To get from chord tone to chord tone there are passing tones off the beat. You’ll notice that the lower passing notes are the same as the major scale, but because the dominant 7 is a tone away from the next chord tone (the root) it is necessary to put in a passing chromatic note. When playing over a Dominant chord it is important that the major 7 passing note is only ever placed off the beat and you should treat it as an “avoid” note in your solos.
Here is a Musescore file with the C Bebop Scale from the root, 3rd, 5th, and 7th.
Jazz tonguing
When practising the Bebop scale it’s a good chance to reinforce your jazz tonguing by making sure you’re tonguing off-beat notes and playing smoothly through the phrases without any short clipped notes which will result in a very lumpy, uncool swing feel and restrict your ability to play at speed. Here’s an example of an exercise to introduce you to jazz tonguing or revisit it if you find you’re leaving gaps in your phrases.
Once you have some familiarity with the scale from the Root why not try playing along with this backing track (Set it to 0.75 Speed as full speed may be a bit fast initially)