From my perspective how I see them is exes (pretty much confirmed by Charley) who hated each other irrationally for the longest time (like most exes do) then became and are currently very close friends verging on a couple.

I think currently that there is some romance there but more unrequited love on Holden's part. He would do anything for Bebop, but Bebop seems too invested in other things and while he does care deeply for Holden I don't think he's willing to take the time to be with him right now.