all based on feels
Ornette Coleman said:
"Music is for our feelings."
So it's ok that you keep mentioning, talking about how important it 'feels' to you when you listen to a piece/recording of music.
One thing to remember about most modern jazz, particularly bebop and (so-called 1950s/60s) post-bop: It follows a prescribed structure.
In "Strode Rode" and all other bop tunes or jazz standards of this genre, the essential structure is
1. State the melody (by the leader on horn or piano)
2. several bars of an instrumental solo, which follows and stays within the *chord structure* foundation of the melody, but does not adhere to the note pattern of the song's melody itself
3. Bridge (if the song/composition happens to have one)
4. instrumental solo (as above)
5. Return to melody again for final statement/finish of the song
Sometimes at the end of these bop tunes and small group ensembles playing them, the drummer will have a 'trading fours' (meaning that the drummer shares four bars with another instrumentalist, back-and-forth) segment near the end of the song.
Does that help?
bass and the main instrument
As mentioned above, the bop and post-bop music is founded upon bass and drums. Rhythm is the basis of bebop, the bass player and drummer drive the group, the song, and the sound. They are the foundation, like the foundation of a house, in this music. It was the same for the preceding 1930s-era swing jazz music: bassist and drummer were the foundation for the swing orchestra. Piano player is also considered the 'third' part of the rhythm section in jazz. (Piano trio groups, in the 1940s and later bop era, also became a popular type of ensemble playing instrumental jazz music)
For this kind of music it's only needed that you follow, be familiar with the basic tune, and then the music/musicians take you to other places (the improvised solos) during the playing of the tune, in specific segments within the song.