I know that the Cowboy Bebop manga was written and produced by someone other than Shinichiro Watanabe (although the English credits say: Cooperation: Shinichiro Watanabe / Sunrise); the manga Cowboy Bebop, shortly after the TV series ended, and that for all intents and purposes, they are the same canon as the TV series and movie; and the manga Cowboy Bebop: Shooting Star, which was written alongside the original TV series airing. The chapters themselves are pretty similar to an episode of the TV series, so are there specific time frames, or episodes that these chapters are reported to take place? Or is it ambiguous and can safely sit somewhere in the middle of the series (after all the cast have been introduced and are together, before the cast start separating)? Is "Shooting Star" on a completely different timeline?
There are actually two mangas for Cowboy Bebop:
- Cowboy Bebop: Shooting Star
This one is supposed to be an alternative telling of the anime series' story. This one has elements of the story as told in the anime and some entirely new elements.
Being 'a new take' on the anime, I guess this one is supposed to replace its timeline.
Source 1 and 2
- Cowboy Bebop
This one features side-stories, which are supposed to be separate from the anime story.
According to Anime News Network, this one is supposed to take place before the ending of the series (but they do not cite any references). It could fit somewhat like the movie does.