Generally, a piece of music has it’s “ideal tempo” or tempo range. Most music is composed with a certain tempo (expressed in bpm/ beats per minute) in mind. This doesn’t mean that a tune cannot be played in a, sometimes radically, different tempo. A very good example is Lo-Fang’s version of “You’re The One That I Want” from the movie Grease (I dig both his and the original version, but his version blew me away from the first note).
One thing struck me during my musical education and “career”: the players that succeeded to “play the changes” in their solos earlier than anyone else were bass players. They were not only faster to do this regarding fresh (new) tunes, but they could do this sooner in their development as a musician. This doesn’t mean they play the most interesting solos, but just (at least) solos that sounded more “right”.