So ... what is this thing called swing? Swing is the thing that makes it cool ... yes? Anyway, if your wanting your music to swing ... and it doesn't ... then simply follow the ideas which follow. Just remember that this swing thing is one of those "things" in life where ya have to just figure it out for yourself ... learn it on your own ... so it lives in your heart.
In this text, the idea of "swing" in music is purely rhythmic. That any pitch, chord or line can swing is contingent on the way it grooves with the rhythm. Almost always in 4 / 4 time, we get the music to swing by first locking in on the 2 and 4 beats of the measure. Simply find your groove, count the beats 1 2 3 4 ... and add your best version of snapping your fingers sound to your 2 and 4 counting. Do this for a couple of months. When ya see the Cat who strolls along groovin in this manner, follow them and try to emulate their swing. It's fun, even if just for a few moments.
When you and your band get bored doing this, keep counting and snapping, and start to sing your lines. The swing trick is eventually how we each "stretch out" the pulses between each other, creating a kind of elasticity like a rubber band. You hold one end of it and the band has the other. As the pulse grooves along, we create the swing thing by increasing or relaxing the rhythmic tension on this imaginary rubber band. Lock in first always, pulse to pulse ... then gradually pull the time.
I learned how to swing by listening to a Stan Getz record and simply singing along. It was fun to learn the lines and get the groove in me soul. Took a couple of weeks. So maybe cue up your favorite player doin their swing thing and as the song goes ... sing, sing, sing.
In getting your lines to swing ... if you can sing it, you'll swing it. It's just a matter of finding the rhythms and pitches on your ax. So shedding? Yep, it all comes down to the shedding.
"It don't mean a thing if it ain't got that swing."
Duke Ellington