Hi all. I'm a 1 year newbie to bass but I have played saxophone for about 8 years. I am an active member of local jazz groups. These are my few cents on the topic.
The bebop sound cannot be summed up with one scale. It is defined by free expression. In bebop tunes, you have complete melodic freedom. The chord progressions provide structure but the soloist is free to play anything. This means that you are never restricted to specific scales, can be as chromatic as you like, can embellish/distort parts of the melody, can quote other songs, can play out of time, can repeat an idea indefinitely, can superimpose odd time signatures, can be flashy, can be random, etc. In short, you play whatever you want as long as you convey some sort of emotion or idea.
This level of freedom means that there are infinite approaches to playing bebop. The primary approach would be listening and emulating. Books and videos can be used as supplements but it ultimately comes down to listening and playing. So find a musician you like (doesn't even need to be a bassist) and follow their lead.