I live in improv-land. It comes so natural to me… so much so that when I hear a jazz or blues chord progression I put my violin and bow in place and just… play. I started doing improvisation during my high school years (early 70s) and continued jamming, with one long break, until now.
There is a way, I think, that you may want to think about as a way to practice jamming. Go to your favorite online streaming music station (I like Pandora) and play along with the music channel which suits the genre of jam you want to practice.
I jam every Monday night as the “house fiddler” for the “Monday Night Band”.