You've made a couple of wrong assumptions, namely, 1.) thinking it was something you just don't practice, and 2.) guessing it just gets better, the more you do it.
I'll take the second first - it doesn't necessarily get better the more you do it, if you are doing it aimlessly. You need to have enough knowledge of what you are doing so that you can reflect on it each time you do it and make it better the next time. Otherwise you'll just be repeating the same old stuff. FWIW, experienced players can have the same dilemma, just on a different level.
Now to the first assumption. There are players who have great ears and who can pick up all kinds of things naturally. If you are already totally absorbed in jazz and have great ears and natural talent, the following does not apply to you.
If you are a mere mortal like many of us you might need the following advice:
Improvisation is an art and you need the tools.
- an internalised feel for the rhythms
- a sense of the history of the music
- a role model, in person or by proxy (e.g. a person who has the musical characteristics you most want to reflect in your playing).
To do this you need to:
- listen voraciously to the music so that the sounds, rhythms and style become second nature
- transcribe solos so that you can see/hear how the musicians actually articulate an idea, colour the tones, construct ideas
- get one of the standard "how to" books that take you step by step through the process, hopefully with play-along recordings
My advice, if this is all new to you, and not to be overwhelmed with information, is to get Jerry Coker's "How to Practice Jazz". It's a small, concise book that is to the point and perfect for novices. It puts what I just wrote in an organised and easy to understand way.
I would supplement that with Coker's "Improvising Jazz" which then, is a primer on what tools are needed for improvising. Again, it is laid out in a logical manner. I just recommend these books because it saves you and us going over the same ground for a protracted period and also, you then have them for reference whenever you need them.
Many would probably suggest your going with what has become known as the scale/chord method, which is basically, a progressively easy to more advanced way of learning to handle what scales go with what chord and this is usually associated with the Jamey Aebersold Play-along series. Namely:
Volume !. "How to Play Jazz and Improvise".
After you are comfortable with that, next could come vol. 2. "Nothin but Blues" a relatively easy and fun play-along.
Then I think most choose vol 54 "Maiden Voyage" or vol. 5 "Time to Play Music"
That should give you an overview to think about while others are preparing their pet answers to your question. :bluewink: