Yeah, the first 4 episodes are pretty standalone (though they do introduce Ein and Faye), but you really get a glimpse of Spike's backstory and the loose arc for the rest of the series in episode 5.

Alternatively, you could check out the Cowboy Bebop movie. It's set after episode 22 (or thereabouts), but it's a standalone - not referenced in the series at all, and it was produced afterwards. Basically, it's outside the continuity of the series.

But it's just as good as the series. So if you don't like the movie, I seriously doubt you'll enjoy the rest of the show.