If you are reading this manga, then you should have already seen the anime, for unlike most manga, which typically lead to an anime, Cowboy Bebop supplies side stories to the anime and has none of the content that the anime has in terms of backstory or character development that was seen in the anime. Interestingly, the publication is classified as a shoujo, but it has no hallmarks of being such, with the exception of vaguely Banana Fish style artwork. As I have said the manga captures the feel of the anime, but seems to lack just a little something. I feel this something may be the action and the theme selection, which really bring the anime to life. Of course,it is impossible to have music set to the manga, unless it played on a video to music, but isn't that what the anime is for to begin with? That said Cowboy Bebop is a wonderful anime and please check out my anime review here. You can find information on the characters and premise there. Recommended to close fans of the anime.
As a side note, there is a second series Cowboy Bebop: Shooting Star, I have heard mixed things about this series and is somewhat difficult to obtain. I may read it on a scan website(?) (somewhat) soon. Stay tuned!