Great topic!

Bernie lots of great suggestions so far. Let me just describe one approach: It's called "filling in the holes" . This concept was first brought to my attention by a drum teacher actually. His name is Steve Houghton and he was playing in Woody Herman's big when he was still in high school. The guy can play!

Anyways, maybe start with a blues tune like "Kansas City"

Sing the opening line "I'm going to Kansas City-Kansas Here I come"

After you sing that, you then have two bars in which you can fill in that space. Try all sorts of approaches: busy blue scale runs, simple blue scale runs, rhythmic chords stabs, combination of chords and runs.....

You can do this with any tune.... just fill in the "holes"

So in other words, when there is a space in the melody line, you’re going to "fill in the holes"

Hope this makes sense- have fun!