With bebop, there aren't really any 'wrong notes' and so the only way to determine if a song is 'bad' is if the song is able to keep some thematic sense and doesn't devolve into a couple of saxes, a drummer and a pianist playing solos. The 'music' is the reaction you get, not so much the notes being played.

As far as I know, it helps knowing jazz standards to better appreciate the virtuosity of the musicians. That being said, I haven't made time to listen to those standards.

In the case of 'My Favorite Things', Coltrane was able to take something poetic and romantic and turn it into the feeling someone has when their head catches on fire. (side note: Is 'My Favorite Things' about heroin?)

In that case, bebop seems to have unintentionally birthed a style that hip-hop grew into 30 years later - recontexting older music.