The innovations of Charlie Parker and Dizzy Gillespie in the 1940s changed jazz forever. These two guys codified how the language should be spoken. This scale is one result of their efforts. This particular term for the scale was coined by David Baker, so I use it myself.
The Bebop Dominant Scale is basically a Mixolydian mode with an extra note -- a natural 7th. Here is the basic C Mixolydian mode:
The Bebop Dominant has the extra natural 7th, like so:
This added note does two things: 1) Provides a smooth descending leading tone, 2) gives the scale 8 notes. Item 1 is immediately obvious. Item 2 is not apparent until you start soloing with the scale. What the 8 notes do is give you the ability to play chord tones on all downbeats. This is important; it is the most effective way to get long phrases. For example, check out this standard Mixolydian lick:
Notice how the last half starts to sound awkward. You don't have chord tones on downbeats. Look at this bebop lick:
Do you hear it? It just wants to keep going. That's how those guys like Parker, Gillespie, Adderley, etc. could get those endless lines. Even Pat Martino uses this technique. Remember this however: Use the added 7th ONLY when descending. Skip it when you ascend. And KEEP THE CHORDTONES ON DOWNBEATS! By the way, I highly recommend David Baker's 3 volume set on how to play Bebop.
This little device can revolutionize your playing if you take time with it. It can change how you view improvisation. I am not kidding. The Bebop technique is one of the secrets of the masters. Take this one home and lock yourself in a room for a week. Experiment. Make your own licks. Create lines. Then, go get a gig!