A few weeks ago I had a gig with a drummer and a sax player, where I was responsible for all of the chordal comping, both behind the Sax player and also behind my own soloing.
I discovered that it was a lot more difficult than I thought to be the only chordal instrument in the group (and the only bass player, and one of the main soloists as well). So it felt like I had to go back to the drawing board again.
The big problem for me is that when I switch between soloing and comping, my mind has to switch gears in a pretty big way. I called Ondrej Pivec to ask him about this, and he had a lot of great ideas. One thing he said is that as I walk around all day with music in my head, incorporate chords as part of the melody. Also, think of chords as harmonized melody.
As an exercise, I’ve been working comping into my bebop practice. 2 bars soloing, then two bars comping. Not necessarily starting on the first measure. It sounds really cool.