Yeah, mainly the characters are drawn by cels.  
Certain background elements, mechanicial stuffs, 
special effects are done on computers.  From what 
I know (talked with Toshihiro Kawamoto, the 
character designer of Cowboy Bebop), most 
backgrounds are hand-painted actually.  But 
somehow, the studios released most of them in 
laser-copies.  I guess they can make more money 
this way.