People are often intimidated by the word Improvising. I think this is sometimes due to the incorrect notion that you must play something complicated. People incorrectly believe that it’s something you make up on the spot, that you’ve never played or practiced before.
Improvising ~ How can you do this?
Yet, improvising can be BABY STEPS (To quote “What about Bob”). You can take something like “Cripple Creek” and begin by changing one little piece of it.
For example, change where you play the C chord. Instead of playing it at the 2nd fret, try playing it at the 5th fret.
You can also improvise with the right-hand by changing the rolls. Try using an alternating thumb roll on the C chord instead of your usual pattern. Try a variety of roll patterns.
The sooner you get your mind out of one locked way of doing things, the better off you will be when it comes to improvising.
In summary, begin by changing where you play the chord on the neck or change the roll pattern. If it is difficult, then you are trying to change too many things. Remember, baby steps. Keep it super simple!
After you do this for awhile, one day you will be able to spontaneously choose which one of these variations you want to do. Each variation has to be practiced over and over until it requires no thought. It can be quite a joy to sit around and see how many different variations you can play of a section over and over. Try it!